Learning Materials
Features
Discover
Chapter 6: Problem 58
If \(e^{x}+e^{y}=e^{x+y}\), prove that, \(\frac{d y}{d x}+e^{y-x}=0\)
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 \(f(x)=1+x^{3}\). If \(g(x)=f^{-1}(x)\), then prove that \(g^{\prime \prime \prime}(2)=\frac{8}{3}\)
The number of roots of the equation \(\sin x+2 \sin 2 x\) \(+3 \sin 3 x=0\) is the interval \([0, \pi]\) is (a) 1 (b) 2 (c) 3 (d) More than 3
If \(x=a \cos \theta, y=b \sin \theta\), find \(\frac{d^{2} y}{d x^{2}}\)
If \(\int_{0}^{1} e^{x}(x-\alpha) d x=0\), then (a) \(1<\alpha<2\) (b) \(\alpha \leq 2\) (c) \(0<\alpha<1\) (d) \(\alpha=0\)
Let \(f\) be differentiable for all \(x\). If \(f(1)=-2\) and \(f^{\prime}(x) \geq 2\) for all \(x \in[1,6]\) then (a) \(f(6)<8\) (b) \(f(6)>8\) (c) \(f(6)>5\) (d) None
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