Question
Hint:
Finding limits for the vast majority of points for a given function is as simple as substituting the number that x approaches into the function. In this question, we have to find value of
.
The correct answer is: ![straight pi over 3](data:image/png;base64,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)
![stack L t with x not stretchy rightwards arrow negative 1.5 below cos to the power of negative 1 end exponent space open parentheses fraction numerator x plus 3 over denominator 3 end fraction close parentheses](data:image/png;base64,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)
On substituting, We get
( Value of
= π/6 )
![stack L t with x not stretchy rightwards arrow negative 1.5 below straight pi over 6 space space T h e r e f o r e comma space fraction numerator straight pi over denominator 6 space end fraction space i s space t h e space f i n a l space a n s w e r.](data:image/png;base64,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)
A limit is the value that the output of a function approaches as the input of the function approaches a given value.
Related Questions to study
The force required to stretch a steel wire of 1 cm2 cross-section to 1.1 times its length would be ![open parentheses straight Y equals 2 cross times 10 to the power of 11 straight N over straight m squared close parentheses](data:image/png;base64,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)
The force required to stretch a steel wire of 1 cm2 cross-section to 1.1 times its length would be ![open parentheses straight Y equals 2 cross times 10 to the power of 11 straight N over straight m squared close parentheses](data:image/png;base64,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)
Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if = n, in which case one writes x =
.
Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if = n, in which case one writes x =
.
The graph shows how the magnification m produced by a convex thin lens varies with image distance v. What was the focal length of the used
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)
The graph shows how the magnification m produced by a convex thin lens varies with image distance v. What was the focal length of the used
![](data:image/png;base64,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)
The graph shows variation of v with change in u for a mirror. Points plotted above the point P on the curve are for values of v
![](data:image/png;base64,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)
The graph shows variation of v with change in u for a mirror. Points plotted above the point P on the curve are for values of v
![](data:image/png;base64,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)
When light is incident on a medium at angle i and refracted into a second medium at an angle r, the graph of sin i vs sin r is as shown in the graph. From this, one can conclude that
![](data:image/png;base64,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)
When light is incident on a medium at angle i and refracted into a second medium at an angle r, the graph of sin i vs sin r is as shown in the graph. From this, one can conclude that
![](data:image/png;base64,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)
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
We can only apply the L’Hospital’s rule if the direct substitution returns an indeterminate form, that means
The value of on using simpson's 3rd rule by taking h=1 is [Given
The value of on using simpson's 3rd rule by taking h=1 is [Given