Learning Materials
Features
Discover
Chapter 3: Problem 24
If \(\mathrm{y}=|1-| 2-|3-| 4-\mathrm{x}|||| ;\) then number of points where \(\mathrm{y}\) is not differentiable; is (A) 1 (B) 3 (C) 5 (D) \(>5\)
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Let \(f: R \rightarrow R, f(x-f(y))=f(f(y))+x f(y)+f(x)-1 \forall x\), \(y \in R\), if \(f(0)=1\) and \(f^{\prime}(0)=0\), then (A) \(\mathrm{f}(\mathrm{x})=1-\frac{\mathrm{x}^{2}}{2}\) (B) \(f(x)=x^{2}+1\) (C) \(f(x)=\left(\frac{2 x+1}{x+1}\right)\) (D) none of these
If \(f(x)=\operatorname{Max} \cdot\\{1,(\cos x+\sin x)\) \((\sin x-\cos x)\\} 0 \leq x \leq 5 \pi / 4\), then (A) \(\mathrm{f}(\mathrm{x})\) is not differentiable at \(\mathrm{x}=\pi / 6\) (B) \(f(x)\) is not differentiable at \(x=5 \pi / 6\) (C) \(f(x)\) is continuous for \(x \in[0,5 \pi / 4]\) (D) None of these
The number of points where the function \(f(x)=\left(x^{2}-1\right)\left|x^{2}-x-2\right|+\sin (|x|)\) is not differentiable is (A) 0 (B) \(I\) (C) 2 (D) 3
If \(f(x)=\frac{x}{1+e^{1 / x}}, x \neq 0\) and \(f(0)=0\) then, (A) \(f(x)\) is continuous at \(x=0\) and \(f^{\prime}(x)=1\) (B) \(\mathrm{f}(\mathrm{x})\) is discontinuous at \(\mathrm{x}=0\) (C) \(\mathrm{f}(\mathrm{x})\) is continuous at \(\mathrm{x}=0\) and \(\mathrm{f}^{\prime}(\mathrm{x})\) does not exists (D) \(f(x)\) is continuous at \(x=0\) and \(f^{\prime}(x)=0\)
The number of points on \([0,2]\) where $f(x)= \begin{cases}x\\{x\\}+1 & 0 \leq x<1 \\ 2-\\{x\\} & 1 \leq x \leq 2\end{cases}$ fails to be continuous or derivable is (A) 0 (B) 1 (C) 2 (D) 3
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine