Category: class 12

22. If (y=e^{a{cos}^{-1}{x}}), (-1le xle1), show that (left(1-x^2right)frac{d^2y}{dx^2}-xfrac{dy}{dx}-a^2y=0). Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity

21. If (y=left|begin{matrix}fleft(xright)&gleft(xright)&hleft(xright)\l&m&n\a&b&c\end{matrix}right|), prove that (frac{dy}{dx}=left|begin{matrix}f'(x)&g'(x)&h'(x)\l&m&n\a&b&c\end{matrix}right|). Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability

20. Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify

19. Using the fact that (sin{(A+B)}=sin{A}cos{B}+cos{A}sin{B}) and the differentiation, obtain the sum formula for cosines. Continuity and Differentiability

18. If (fleft(xright)=left|xright|^3), show that f”(x) exists for all real x and find it. Continuity and Differentiability Miscellaneous

17. If (x=aleft(cos{t}+tsin{t}right) ) and (y=aleft(sin{t}-tcos{t}right)), find (frac{d^2y}{dx^2}). Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity

16. If (cos{y}=xcos{left(a+yright)} ) with (cos{a}neqpm1), prove that (frac{dy}{dx}=frac{{cos}^2{left(a+yright)}}{sin{a}}). Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12

15. If (left(x-aright)^2+left(y-bright)^2=c^2), for some c>0, prove that (frac{left[1+left(frac{dy}{dx}right)^2right]^frac{3}{2}}{frac{d^2y}{dx^2}}) is a constant independent of a and b. Continuity

14. If (xsqrt{1+y}+ysqrt{1+x}=0), for (-1<x<1), prove that (frac{dy}{dx}=-frac{1}{left(1+xright)^2}). Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity

13. Find (frac{dy}{dx}), If (y={sin}^{-1}{x}+{sin}^{-1}{sqrt{1-x^2}}),(-1le xle1). Continuity and Differentiability Miscellaneous Exercise Previous Next Class 12 Continuity and Differentiability