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If \[f\left( x \right) = \begin{cases}\frac{\sin \left( \cos x \right) - \cos x}{\left( \pi - 2x \right)^2}, & x \neq \frac{\pi}{2} \\ k , & x = \frac{\pi}{2}\end{cases}\]is continuous at x = π/2, then k is equal to
Concept: undefined >> undefined
Show that f(x) = |x − 2| is continuous but not differentiable at x = 2.
Concept: undefined >> undefined
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Show that f(x) = x1/3 is not differentiable at x = 0.
Concept: undefined >> undefined
Show that \[f\left( x \right) =\]`{(12x, -,13, if , x≤3),(2x^2, +,5, if x,>3):}` is differentiable at x = 3. Also, find f'(3).
Concept: undefined >> undefined
Show that the function f defined as follows, is continuous at x = 2, but not differentiable thereat:
Concept: undefined >> undefined
Find whether the function is differentiable at x = 1 and x = 2
Concept: undefined >> undefined
Show that the function
(i) differentiable at x = 0, if m > 1
(ii) continuous but not differentiable at x = 0, if 0 < m < 1
(iii) neither continuous nor differentiable, if m ≤ 0
Concept: undefined >> undefined
Show that the function
\[f\left( x \right) = \begin{cases}\left| 2x - 3 \right| \left[ x \right], & x \geq 1 \\ \sin \left( \frac{\pi x}{2} \right), & x < 1\end{cases}\] is continuous but not differentiable at x = 1.
Concept: undefined >> undefined
If \[f\left( x \right) = \begin{cases}a x^2 - b, & \text { if }\left| x \right| < 1 \\ \frac{1}{\left| x \right|} , & \text { if }\left| x \right| \geq 1\end{cases}\] is differentiable at x = 1, find a, b.
Concept: undefined >> undefined
If f is defined by f (x) = x2, find f'(2).
Concept: undefined >> undefined
Write an example of a function which is everywhere continuous but fails to differentiable exactly at five points.
Concept: undefined >> undefined
Discuss the continuity and differentiability of f (x) = |log |x||.
Concept: undefined >> undefined
Discuss the continuity and differentiability of f (x) = e|x| .
Concept: undefined >> undefined
Discuss the continuity and differentiability of
Concept: undefined >> undefined
Define differentiability of a function at a point.
Concept: undefined >> undefined
Is every differentiable function continuous?
Concept: undefined >> undefined
Is every continuous function differentiable?
Concept: undefined >> undefined
Give an example of a function which is continuos but not differentiable at at a point.
Concept: undefined >> undefined
If f (x) is differentiable at x = c, then write the value of
Concept: undefined >> undefined
Write the points where f (x) = |loge x| is not differentiable.
Concept: undefined >> undefined
