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Solution for the question - 4(xrarr0)(sqrt({:(1+x)-sqrt((1+x^(2):}))))//(sqrt({:(1-x^(2))-sqrt((1-x)))):} 1//2 '/> -1 '/>01

4(x rarr0)(sqrt({:(1+x)-sqrt((1+x^(2):}))))//(sqrt({:(1-x^(2))--Turito

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Solution for the question - u(x rarr0)(sqrt({:((1+x+x^(2)))-1)//x):} 0211//2 '/>

U(x rarr0)(sqrt({:((1+x+x^(2)))-1)//x):} -Turito

In this given question we have to find limit of <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x minus greater than 3 of fraction numerator x cubed minus 8 x squared plus 45 over denominator 2 x squared minus 3 x minus 9 end fraction" width="153" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mn»3«/mn»«/mrow»«/munder»«mfrac»«mrow»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»8«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»45«/mn»«/mrow»«mrow»«mn»2«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mn»9«/mn»«/mrow»«/mfrac»«/math»'/> Step1: Finding the limit. The limit can be found out by differentiating both numerator and denominator as we are getting <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAJtJREFUeNpjYMAN+IB4GhCfhOKZUDGSwV4g9kPi+0DFSAKhQDwJi/gEII4kxaA1QOyGRdwRKkc0eAfEbFjEQWIvSTHoDx65X9Qy6AcpBr3E4TUOUr0GClAPLOJupAZ2EBDPxiI+n9ToB4H9QFwAxCxQb1YD8UFyUrYgEM+FBu43aBbhYRgFgwv8JxOPgsEERquj0epotDqiXnUEAHl3QY/fxbExAAAAYnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MDwvbW4+PG1uPjA8L21uPjwvbWZyYWM+PC9tYXRoPt4dSgEAAAAASUVORK5CYII=" class="Wirisformula" alt="0 over 0" width="18" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»0«/mn»«mn»0«/mn»«/mfrac»«/math»'/> form. =&gt; <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x minus greater than 3 of fraction numerator 3 x squared minus 16 x over denominator 4 x minus 3 end fraction" width="128" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mn»3«/mn»«/mrow»«/munder»«mfrac»«mrow»«mn»3«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»16«/mn»«mi»x«/mi»«/mrow»«mrow»«mn»4«/mn»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mfrac»«/math»'/> Now we will put the value of <img src="data:image/png;base64,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" class="Wirisformula" alt="x equals 3" width="38" height="13" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mn»3«/mn»«/math»'/> in both numerator and denominator to find the limit. =&gt; <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x minus greater than 3 of fraction numerator 3 cross times 3 squared minus 16 cross times 3 over denominator 4 cross times 3 minus 3 end fraction" width="160" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»§#62;«/mo»«mn»3«/mn»«/mrow»«/munder»«mfrac»«mrow»«mn»3«/mn»«mo»§#215;«/mo»«msup»«mn»3«/mn»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»16«/mn»«mo»§#215;«/mo»«mn»3«/mn»«/mrow»«mrow»«mn»4«/mn»«mo»§#215;«/mo»«mn»3«/mn»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mfrac»«/math»'/> =&gt; <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator negative 21 over denominator 9 end fraction" width="41" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»-«/mo»«mn»21«/mn»«/mrow»«mn»9«/mn»«/mfrac»«/math»'/> =&gt;<img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator negative 7 over denominator 3 end fraction" width="31" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»-«/mo»«mn»7«/mn»«/mrow»«mn»3«/mn»«/mfrac»«/math»'/>. So, the value of the limit is <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator negative 7 over denominator 3 end fraction" width="31" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»-«/mo»«mn»7«/mn»«/mrow»«mn»3«/mn»«/mfrac»«/math»'/>

Solution for the question - (4x rarr3)(x^(3)-8x^(2)+45)//(2x^(2)-3x-9) (-1)//3 '/> 1//3 '/> (-7)//3 '/> 7//3 '/>

(4x rarr3)(x^(3)-8x^(2)+45)//(2x^(2)-3x-9) -Turito

The given function is f(x) = <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE4AAAAmCAYAAABqDa0qAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAaPUZr5AAAAtxJREFUeNrtWjFIHEEUHQ45REQIIhYigoVFisNOwhFECCEEkSBYWKQQQcTKIhBShCA2wcJC0ohFEAlCEJEgIoiFhBSCBAlBRJCQStJIOFKE42D9n3uLn/HWu72bmb075sHjdmZn9v/59//M7P5RqnasE8eURyxcEAOwB3V9xD1inpgjjqP+nDhKPMG91+I5X4kZXKeI+3hOEnCiSwvxnyg/IP4iTkDoHHEF1wXiBgw8SLwW/digm7heFsZOAk50eUQ8FOVXxCVRfkd8SRyCp4XIav0Yp8R54lodRJJ1XSaJH0V5i/hcKz9Du/V7+il4Jodzug4MZ10XFjAjyuziT8X8wGHcgXazWr9pUX6CvmfEroSNZkSXbnjNf+Jv4rB2/zNCMcQLzGMK9X9xva154o4o9xKPiO2YExctGqXceIzowp7yQ2w1HhJ/am2ymOTT2j/2BvfW4JHcplW0CctprGIDqOfyJRQ3jXLjMabLEgwgsRsz7lvAeoCJ8ZRFCmHWpdXl8JsUggqY6HiGIpT61qAbdWfjGcPE3yxwNh7e2B43keGcjucMu+cUXqV4Yn3cwMZzNp5+LM8FCJ1ucK9rtvF4eHh4eNQzAs+qX+k8PDw8PDw8rOLam6D6/Z1HjZtiHfxllT8Q8lkQPkeSjTA6H4ngjBGn5Tj91lviWfyZ532J+kVl5xOQdXn3edwnVUyzMabU3fRhAKNxhqlPtDuKeN53Vcx9KtH2g0XHsCqv0lBNwfP0viMVtAvBxyWWcc352UPLEWVVXlBD26CKZx6oYoadD750Gni/Loc48owZ7i3mtkKEotUYbh4emXE0j1uTFzXIVcxfrQY9jheXLYTPpAOjWZWXV6Wz3TnDocrJlC/ENlU8r3FiOnRcyzuN+DfOxbLdg2X8St0eaY1jOD6asKcpzicjNywZzYk8XhX/lBhsBst5Hns5PmawgLZxDMeHXrY1g4fYxMpnEkbk3QCJvyTYTITH6wAAAQl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1zdXA+PG1pPmU8L21pPjxtcm93PjxtaT50PC9taT48bWk+YTwvbWk+PG1pPm48L21pPjxtaT54PC9taT48L21yb3c+PC9tc3VwPjxtbz4tPC9tbz48bXN1cD48bWk+ZTwvbWk+PG1pPng8L21pPjwvbXN1cD48L21yb3c+PG1yb3c+PG1pPnRhbjwvbWk+PG1pPng8L21pPjxtbz4tPC9tbz48bWk+eDwvbWk+PC9tcm93PjwvbWZyYWM+PC9tYXRoPqUsi+EAAAAASUVORK5CYII=" class="Wirisformula" alt="fraction numerator e to the power of t a n x end exponent minus e to the power of x over denominator tan x minus x end fraction" width="78" height="38" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msup»«mi»e«/mi»«mrow»«mi»t«/mi»«mi»a«/mi»«mi»n«/mi»«mi»x«/mi»«/mrow»«/msup»«mo»-«/mo»«msup»«mi»e«/mi»«mi»x«/mi»«/msup»«/mrow»«mrow»«mi»tan«/mi»«mi»x«/mi»«mo»-«/mo»«mi»x«/mi»«/mrow»«/mfrac»«/math»'/> <img src="data:image/png;base64,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" class="Wirisformula" alt="limit as x rightwards arrow 0 of f left parenthesis x right parenthesis space equals limit as x rightwards arrow 0 of fraction numerator e to the power of tan x end exponent minus e to the power of x over denominator tan x minus x end fraction

T h e r e space i s space o n e space f o r m u l a space limit as x rightwards arrow 0 of fraction numerator e to the power of x minus 1 over denominator x end fraction equals 1
" width="281" height="112" style="vertical-align:-45px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mn»0«/mn»«/mrow»«/munder»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mn»0«/mn»«/mrow»«/munder»«mfrac»«mrow»«msup»«mi»e«/mi»«mrow»«mi»tan«/mi»«mi»x«/mi»«/mrow»«/msup»«mo»-«/mo»«msup»«mi»e«/mi»«mi»x«/mi»«/msup»«/mrow»«mrow»«mi»tan«/mi»«mi»x«/mi»«mo»-«/mo»«mi»x«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mspace 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class="Wirisformula" alt="limit as x rightwards arrow 0 of f left parenthesis x right parenthesis space equals space limit as x rightwards arrow 0 of fraction numerator e to the power of x left parenthesis e to the power of tan x minus x end exponent minus 1 right parenthesis over denominator tan x minus x end fraction
space space space space space space space space space space space space space space space equals limit as x rightwards arrow 0 of space e to the power of x space cross times space fraction numerator e to the power of tan x minus x end exponent over denominator tan x minus x end fraction
space space space space space space space space space space space space space space space equals e to the power of 0 space end exponent cross times space 1
space space space space space space space space space space space space space space space equals space 1" width="237" height="143" style="vertical-align:-72px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mn»0«/mn»«/mrow»«/munder»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mn»0«/mn»«/mrow»«/munder»«mfrac»«mrow»«msup»«mi»e«/mi»«mi»x«/mi»«/msup»«mo»(«/mo»«msup»«mi»e«/mi»«mrow»«mi»tan«/mi»«mi»x«/mi»«mo»-«/mo»«mi»x«/mi»«/mrow»«/msup»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«mrow»«mi»tan«/mi»«mi»x«/mi»«mo»-«/mo»«mi»x«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»=«/mo»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mn»0«/mn»«/mrow»«/munder»«mo»§#160;«/mo»«msup»«mi»e«/mi»«mi»x«/mi»«/msup»«mo»§#160;«/mo»«mo»§#215;«/mo»«mo»§#160;«/mo»«mfrac»«msup»«mi»e«/mi»«mrow»«mi»tan«/mi»«mi»x«/mi»«mo»-«/mo»«mi»x«/mi»«/mrow»«/msup»«mrow»«mi»tan«/mi»«mi»x«/mi»«mo»-«/mo»«mi»x«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»=«/mo»«msup»«mi»e«/mi»«mrow»«mn»0«/mn»«mo»§#160;«/mo»«/mrow»«/msup»«mo»§#215;«/mo»«mo»§#160;«/mo»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«/math»'/> This is the required answer.

Solution for the question - delta(x rarr0)(e^(tan x)-e^(x))//(tan x-x) 1tan x '/> e^(x) '/>0

Delta(x rarr0)(e^(tan x)-e^(x))//(tan x-x) -Turito

Solution for the question - General 0log 4 '/>1log 2 '/>

General-Turito

Solution for the question - t(x rarr pi//2)(sec x-tan x)//(pi//2-x) pi//2 '/>11//2 '/>2

[t(x rarr pi//2)(sec x-tan x)//(pi//2-x) -Turito

Solution for the question - (t_((x rarr pi//2))[sec 3x cos 5x]:} (-3)//5 '/> 3//5 '/> 5//3 '/> (-5)//3 '/>

(t_((x rarr pi//2))[sec 3x cos 5x]:} -Turito

Solution for the question - 4(x rarr pi//2)[sec 3x cos 5x -3//5 '/> 3//5 '/> (5)//3 '/> (-5)//3 '/>

4(x rarr pi//2)[sec 3x cos 5x] -Turito

K1 and K2 are equilibrium constants for reaction (i) and (ii) <img src="data:image/png;base64,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" class="Wirisformula" alt="N subscript 2 end subscript left parenthesis g right parenthesis plus O subscript 2 end subscript left parenthesis g right parenthesis ℶ 2 N O left parenthesis g right parenthesis" width="167" height="19" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msub»«mrow»«mi»N«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«mo»(«/mo»«mi»g«/mi»«mo»)«/mo»«mo»+«/mo»«msub»«mrow»«mi»O«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«mo»(«/mo»«mi»g«/mi»«mo»)«/mo»«mi»ℶ«/mi»«mn»2«/mn»«mi»N«/mi»«mi»O«/mi»«mo»(«/mo»«mi»g«/mi»«mo»)«/mo»«/math»'/> (i) <img src="data:image/png;base64,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" class="Wirisformula" alt="N O left parenthesis g right parenthesis 1 divided by 2 N subscript 2 end subscript left parenthesis g right parenthesis plus 1 divided by 2 O subscript 2 end subscript left parenthesis g right parenthesis minus" width="222" height="19" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»N«/mi»«mi»O«/mi»«mo»(«/mo»«mi»g«/mi»«mo»)«/mo»«mn»1«/mn»«mo»/«/mo»«mn»2«/mn»«msub»«mrow»«mi»N«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«mo»(«/mo»«mi»g«/mi»«mo»)«/mo»«mo»+«/mo»«mn»1«/mn»«mo»/«/mo»«mn»2«/mn»«msub»«mrow»«mi»O«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msub»«mo»(«/mo»«mi»g«/mi»«mo»)«/mo»«mo»-«/mo»«/math»'/> (ii) Then,

Solution for the question - k1 and k2 are equilibrium constants for reaction (i) and (ii){:n_(2)(g)+o_(2)(g)]2no(g) (i) no(g)1//2n_(2)(g)+1//2o_(2)(g)- (ii) the

K1 and k2 are equilibrium constants for reaction (i) and (ii) -Turito

Solution for the question - 4(x rarr0(x+2)+4)(3(x+1)+4)//3(x+2) 011//3 '/>3

4(x rarr0(x+2)+4)(3(x+1)+4)//3(x+2) -Turito

Solution for the question - ([(x rarr0)(sin^^(-1)x)//x) does not exist201

([(x rarr0)(sin^^(-1)x)//x)] -Turito

Solution for the question - qquad(x rarr b)2x//(tan-1)x) 4201

Qquad(x rarr b)2x//(tan-1)x) -Turito

Solution for the question - (f(x rarr4)(sqrtx-2)//(x-4) 1//4 '/>421//2 '/>

(f(x rarr4)(sqrtx-2)//(x-4) -Turito

Solution for the question - /_(x rarr0)2//x cog(1+x) log x '/>012

/_(x rarr0)2//x cog(1+x) -Turito

Solution for the question - (x rarr0)(1+2x//3)(1//x) theta^(3) '/> e(3//2) '/> e(1//3) '/> e(2//3) '/>

[(x rarr0)(1+2x//3)(1//x) -Turito

Solution for the question - lt_(x rarr-1.5)cos^(-1)((x+3)/(3)) pi//4 '/> pi//3 '/> pi//6 '/> pi//2 '/>

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K1 and K2 are equilibrium constants for reaction (i) and (ii) (i) (ii) Then,

K1 and K2 are equilibrium constants for reaction (i) and (ii) (i) (ii) Then,

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