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question_answer1) Let: \[f:(-1,1)\to R\] be a function defined by \[f(x)=\max \] If K be the set of all points at which f is not differentiable, then the number of elements in the set K is
question_answer2) Suppose \[f(x)\]is differentiable at \[x=1\] and \[\underset{h\to 0}{\mathop{\lim }}\,\frac{1}{h}f(1+h)=5,\], then \[f'(1)\] equal to
question_answer3) Let \[f(a)=g(a)=k\] and their nth derivatives \[{{f}^{n}}(a),{{g}^{n}}(a)\] exist and are not equal for some n. Further if \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(a)g(x)-f(a)-g(a)f(x)+f(a)}{g(x)-f(x)}=4,\] then the value of k is
question_answer4) Let S be the set of all points in \[(-\pi ,\pi )\] at which the function \[f(x)=\min \,\,\{\sin x,\cos x\}\] is not differentiable. Then the number of elements in the set S is
question_answer5) If the function be continuous at \[x=\frac{\pi }{2},\] then k =
question_answer6) If the function is continuous at \[x=0,\] then the value of k is
question_answer7) If the function f defined on by is continuous, then k is equal to
question_answer8) The point at which function \[f(x)=({{x}^{2}}-1)|{{x}^{2}}-3x+2|+\cos (|x|)\] is not differentiable is
question_answer9) Let \[f(x)=15-|x-10|;\] \[x\in R\]. Then the number of elements in the set of all values of x, at which the function, \[g(x)=f(f(x))\] is not differentiable, is
question_answer10) Let \[f(x)=[3+4\sin x]\] (where [ ] denotes the greatest integer function). If sum of all the values of x in \[[\pi ,2\pi ],\]where \[f(x)\]fails to be differentiable, is \[\frac{k\pi }{2},\] then the value of k is
question_answer11) Let : \[f:[-1,3]'!R\] be defined as where [t] denotes the greatest integer less than or equal to t. Then, the number of points at which f is discontinuous are
question_answer12) The function \[f:R/\{0\}\to R\] given by can be made continuous at \[x=0\] by defining \[f(0)\] as
question_answer13) The derivative of with respect to \[\frac{x}{2},\]where is
question_answer14) Let If \[f(x)\] is continuous in \[\left[ 0,\,\,\frac{\pi }{2} \right]\], then is
question_answer15) If \[f(x+y)=f(x).f(y)\forall x.y\] and \[f(5)=2,\,\,f'(0)=3,\] then \[f'(5)\]is
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