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Differentiate the following functions wi...

Differentiate the following functions with respect to `xdot` `x^(2/3)+7e-5/x+7tanx` (ii) `x^2dotlnxdote^x` `lntan(pi/4+x/2)` (iv) `(s in x-x cos x)/(x s in x+cos x)` `tan(tan^(-1)sqrt((1-cosx)/(1+cosx))),0

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RESONANCE DPP-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Find (dy)/(dx) if: x=a(cos t+1/2lntan^2t/2) and y=asintdot x=s in tsq...

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  2. Differentiate the given functions w.r.t.x. (ln"x")^(cos"x") (ii) x^x-...

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  3. Differentiate the following functions with respect to xdot x^(2/3)+7e...

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  4. If y="sec"(tan^(-1)x), then (dy)/(dx) at x=1 is equal to: 1/(sqrt(2)) ...

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  5. Find (dy)/(dx) in each of the following cases: y=tan^(-1)(4x)/(1+5x^2...

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  6. If f^(prime)(x)=sqrt(2x^2-1) and f(x^2), then (dy)/(dx) at x=1 is equa...

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  7. Find (dy)/(dx), when xa n dy are connected by the following relations ...

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  8. Let f(x)={(sina x^2)/(x^2); x!=0 and 3/4+1/(4a); x=0dot For what v...

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  9. If y=A e^(-k t)cos(p t+c), then prove that (d^2y)/(dt^2)+2k(dy)/(dx)+n...

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  10. (d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2))^-1 (2) -((d^2y)/(dx^2))^-1...

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  11. If x=a t^2,y=2a t , then (d^2y)/(dx^2) is equal to (a)-1/(t^2) (b...

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  12. If x=(1+t)/(t^3),y=3/(2t^2)+2/t , then x((dy)/(dx))^3-(dy)/(dx) is e...

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  13. If e^y(x+1)=1, show that (d^(2y))/(dx^2)=((dy)/(dx))^2 If y=sin(2sin^...

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  14. Evaluate : ("lim")(xvec2a^+)(sqrt(x-2a)+sqrt(x)-sqrt(2a))/(x^2-4a^2)

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  15. Evaluate: ("lim")(xvec2a^+)((e^x I n(2^(x-1))-(2^x-1)^xsinx)/(e^(x I n...

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  16. If f^(prime)(k)=l ,t h e nl= 0 (b) 4/5 (c) pi/2 (d) (16)/5

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  17. f^(prime)(l+3)= 0 (b) 2/5 (c) -2/5 (d) -4/5

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  18. Comprehension (for Q. No. 1 to 3) Let f(x)=sin^(-1)(1-x^2)/(1+x^2)+tan...

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  19. Solve for x , if [cos^(-1)x]=[sin^(-1)x] (where [.] represents greates...

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  20. underset(x to0)(lim)((1+a^(3))+8e^(1//x))/(1+(1-b^(3))e^(1//x))=2 " th...

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