Maths-
General
Easy
Question
If
then k=
- 0
![negative 1 third](data:image/png;base64,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)
![2 over 3](data:image/png;base64,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)
![fraction numerator negative 2 over denominator 3 end fraction](data:image/png;base64,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)
Hint:
In the question we will first use L hospital theorem,
, in LHS. Then we will use the value of x to get the value of k.
The correct answer is: ![2 over 3](data:image/png;base64,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)
![L straight t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator log begin display style space end style left parenthesis 3 plus x right parenthesis minus log space left parenthesis 3 minus x right parenthesis over denominator x end fraction equals k](data:image/png;base64,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)
L.H.S=![L straight t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator log begin display style space end style left parenthesis 3 plus x right parenthesis minus log space left parenthesis 3 minus x right parenthesis over denominator x end fraction](data:image/png;base64,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)
using L hospital theorem,
![L straight t subscript x not stretchy rightwards arrow 0 end subscript fraction numerator begin display style fraction numerator d blank over denominator d straight x end fraction end style log begin display style space end style left parenthesis 3 plus x right parenthesis minus begin display style fraction numerator d blank over denominator d x end fraction end style log space left parenthesis 3 minus x right parenthesis over denominator begin display style fraction numerator d blank over denominator d x end fraction end style x end fraction
equals Lt subscript straight x not stretchy rightwards arrow 0 end subscript fraction numerator begin display style fraction numerator 1 over denominator 3 plus straight x end fraction end style plus begin display style fraction numerator 1 over denominator 3 minus straight x end fraction end style over denominator 1 end fraction
equals Lt subscript straight x not stretchy rightwards arrow 0 end subscript fraction numerator 3 minus straight x plus 3 plus straight x over denominator left parenthesis 3 plus straight x right parenthesis left parenthesis 3 minus straight x right parenthesis end fraction
equals Lt subscript straight x not stretchy rightwards arrow 0 end subscript fraction numerator 6 over denominator 9 plus straight x squared end fraction
equals fraction numerator 6 over denominator 9 plus 0 end fraction
equals 6 over 9 equals 2 over 3](data:image/png;base64,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)
So, k=![2 over 3](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAN1JREFUeNpjYMAOrIF4DRB/AuJfQHwBiKMZyAAHgTgSiHmgfC0gPgoVoxjIA/ElBiqBH9QwxBLqPYoABxCfhEYC2UAQiDcAsRslhihBDVGhxBANIJ4NxFyUGCIOxKuAmIXSwN0CdRHF4D8ePAoGE/hPJh4FgwU4AvE2IP4GLadvAfEEIBYm1aD9QBwExGxIYgZAvINaLv1EDUNAxe4NSkvLRGg4eVEjyxRQ6iVQdRQArdfsqRFGPFDDBk/drwcNcJLbR6HQeo0JmtLvA3E8qQbZQuu2H1AMSuk++DQAAI82PNCcRsQTAAAAYnRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bW4+MjwvbW4+PG1uPjM8L21uPjwvbWZyYWM+PC9tYXRoPrjMGUAAAAAASUVORK5CYII=)
Related Questions to study
maths-
Let
and
be the distinct roots of
then ![fraction numerator L t over denominator x plus a end fraction fraction numerator 1 minus cos space open parentheses a x squared plus b x plus c close parentheses over denominator left parenthesis x minus alpha right parenthesis squared end fraction](data:image/png;base64,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)
Let
and
be the distinct roots of
then ![fraction numerator L t over denominator x plus a end fraction fraction numerator 1 minus cos space open parentheses a x squared plus b x plus c close parentheses over denominator left parenthesis x minus alpha right parenthesis squared end fraction](data:image/png;base64,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)
maths-General
Maths-
In ![straight capital delta A B C comma sum a cubed sin invisible function application left parenthesis B minus C right parenthesis equals](data:image/png;base64,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)
In ![straight capital delta A B C comma sum a cubed sin invisible function application left parenthesis B minus C right parenthesis equals](data:image/png;base64,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)
Maths-General
maths-
maths-General
Maths-
In ![straight capital delta A B C comma a squared cot invisible function application A plus b squared cot invisible function application B plus C squared cot invisible function application C equals](data:image/png;base64,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)
In ![straight capital delta A B C comma a squared cot invisible function application A plus b squared cot invisible function application B plus C squared cot invisible function application C equals](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
Maths-General
Maths-
In ![straight triangle A B C comma cot invisible function application A over 2 plus cot invisible function application B over 2 plus cot invisible function application C over 2 equals](data:image/png;base64,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)
In ![straight triangle A B C comma cot invisible function application A over 2 plus cot invisible function application B over 2 plus cot invisible function application C over 2 equals](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
Maths-General
Maths-
In
, cot ![A plus cot invisible function application B plus cot invisible function application C equals](data:image/png;base64,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)
In
, cot ![A plus cot invisible function application B plus cot invisible function application C equals](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
Maths-General
Maths-
Maths-General
General
Elastic potential and gravitational potential energies are equal all the time.
Elastic potential and gravitational potential energies are equal all the time.
GeneralGeneral
Maths-
In
cot ![A plus cot invisible function application B plus cot invisible function application C equals](data:image/png;base64,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)
In
cot ![A plus cot invisible function application B plus cot invisible function application C equals](data:image/png;base64,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)
Maths-General