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Let f (x) be a polynomial in x. The seco...

Let f (x) be a polynomial in x. The second derivative of `f (e ^(x)) ` w.r.t. x is :

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RESONANCE DPP ENGLISH-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Let f (x) be a polynomial in x. The second derivative of f (e ^(x)) w...

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  2. Find the values of a and b if f is continuous at x=0, where f(x)={:...

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  3. Let g be the inverse function of f and f'(x)=(x^(10))/(1+x^(2)). If f(...

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  4. Differentiate tan^(-1)((1+2x)/(1-2x))wdotrdottsqrt(1+4x^2)

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  5. Find (dy)/(dx) : x=a{cost+1/2logt a n^2t/2} and y=asint .

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  6. Differentiate the given functions w.r.t.x. (i) y = (ln"x")^(cos"x") ...

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

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

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  9. y=tan^(-1)""(4x)/(1+5x^(2))+tan^(-1)""(2+3x)/(3-2x)

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  10. If f^(prime)(x)=sqrt(2x^2-1) and y=f(x^2) , then find (dy)/(dx) at x=1...

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

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  12. Let : f(x)={(sina x^2)/(x^2),x!=0 3/4+1/(4a),x=0 for what values of a...

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  13. 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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  14. (d^2x)/(dy^2) equals: ((d^2y)/(dx^2))^(-1) (b) -((d^2y)/(dx^2))^(-1)(...

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  15. 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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  16. 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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  17. If e^y(x+1)=1, show that (d^(2y))/(dx^2)=((dy)/(dx))^2 If y=sin(2sin^...

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

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  19. Evaluate: lim(x to 0^+)((e^(xln(2^(x-1)))-(2^x-1)^xsinx)/(e^(x lnx)))...

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  20. Let f(x)=[(sinx)/x]+[(2sin2x)/x]++[(10sin10 x)/x] (where [.] is the gr...

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