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If ("lim")(tvecx)(e^tf(x)-e^xf(t))/((t-x...

If `("lim")_(tvecx)(e^tf(x)-e^xf(t))/((t-x)(f(x))^2)=2a n df(0)=1/2,` then find the value of `f^(prime)(0)dot` 4 (b) 2 (c) 0 (d) 1

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CENGAGE ENGLISH-LIMITS AND DERIVATIVES-All Questions
  1. if x<1 then 1/(1+x)+(2x)/(1+x^2)+(4x^3)/(1+x^4)+..............oo

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  2. Find the derivative of (sqrt(x)(x+4)^(3/2))/((4x-3)^(4/3))

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  3. If ("lim")(tvecx)(e^tf(x)-e^xf(t))/((t-x)(f(x))^2)=2a n df(0)=1/2, the...

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  4. If y=x^(x^(x^x...oo) , find (dy)/(dx)

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  5. If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx) is equal to (a)(e^(sqr...

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  6. Differentiate sqrt(((x-1)(x-2))/((x-3)(x-4)(x-5))) with respect to x

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  7. If f(x)=|sinx-|cosx||, then the value of f^'(x) at x=(7pi)/6 is (a) ...

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  8. If y=(tanx)^((tanx)^((tanx).... ∞) ,then find (dy)/(dx) at x=pi/4

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  9. If graph of y=f(x) is symmetrical about the y-axis and that of y=g(x)...

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  10. Differentiate the function with respect to x using the first principle...

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  11. If x=t^2,y=t^3,t h e n(d^2y)/(dx^2)= (a)3/2 (b) 3/((4t)) (c) 3/(2...

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  12. Using the first principle, prove that: d/(dx)(f(x)g(x))=f(x)d/(dx)(g(x...

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  13. If y=x+e^x, then (d^2x)/(dy^2) is (a) e^x (b) - e^x/((1+e^x)^3) (c) -e...

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  14. If y=(1+x^(1/4))(1+x^(1/2))(1-x^(1/4)) , then find (dy)/(dx)dot

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  15. Let f(x)=(lim)(h->0)(("sin"(x+h))^(1n(x+h))-(sinx)^(1nx))/hdot Then f...

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  16. If f(x)=x|x|, then prove that f^(prime)(x)=2|x|

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  17. A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+...

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  18. If y=sqrt((1-cos2x)/(1+cos2x),)x in (0,pi/2)uu(pi/2,pi), then find (dy...

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  19. If x=logp and y=1/p ,then (a)(d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2)+...

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  20. If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)...

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