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Let f(x) be defined as follows: f(x)=[((...

Let `f(x)` be defined as follows: `f(x)=[((cosx-sinx)^(cose cx),-pi/2ltxlt0),(a,x=0),(((e^(1/x)+e^(2/x)+e^(3/x))/(ae^(2x)+be^(3x)),0ltxltpi/2)]` if `f(x)` is continuous `x=0` , then (a)`a=1/e`(b)`a=e`(c) `b=1/e` (d)`b=e`

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

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  2. Let f(x) be defined as follows: f(x)=[((cosx-sinx)^(cose cx),-pi/2ltxl...

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  3. Let g is the inverse function of fa n df^(prime)(x)=(x^(10))/((1+x^2))...

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

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  5. Find (dy)/(dx) if: x=a(cos t+1/2lntan^2t/2) and y=asintdot x=s in tsq...

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

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

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

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

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

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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 and 3/4+1/(4a); x=0dot For what v...

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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: (1) ((d^2y)/(dx^2))^-1 (2) -((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))/(x^2-4a^2)

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

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

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