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Let f(x)=(lim)(h->0)(("sin"(x+h))^(1n(x+...

Let `f(x)=(lim)_(h->0)(("sin"(x+h))^(1n(x+h))-(sinx)^(1nx))/hdot` Then `f(pi/2)` equal to (a)0 (b) equal to 1 (c)In `pi/2` (d) non-existent

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BANSAL-LIMITS AND DERIVATIVES-All Questions
  1. If f((x+2y)/3)=(f(x)+2f(y))/3\ AA\ x ,\ y in R and f^(prime)(0)=1 , f...

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  2. If f is twice differentiable such that f^(x)=-f(x) and f^(prime)(x)=g(...

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

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  4. Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f"(x)-2f'(x)-15f(...

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  5. Let u(x) and v(x) are differentiable functions such that (u(x))/(v(x))...

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  6. A function is represented parametrically by the equations x=(1+t)/(...

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  7. If x=t^3+t+5 & y=sint then (d^2y)/(dx^2)= (a) -((3t^2+1)sint+6tcost)/(...

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

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  9. The equation y^2e^(x y)=9e^(-3) x^2 defines y as a differentiable func...

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  10. A nonzero polynomial with real coefficient has the property that f(x)=...

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  11. If y=x/(sqrt(a^2-1))-2/(sqrt(a^2-1))tan^(-1)((sinx)/(a+sqrt(a^2-1)+cos...

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  12. (lim)(hvec0)((e+h)^(1n(e+h))-e)/hi s

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  13. For the curve represented implicitly as 3^x-2^y=1 , the value of ("Lim...

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  14. If the function f(x)=2-e^(-x) and g(x)=f^(-1)(x) , then the value of g...

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  15. If y^2 = P(x) is polynomial of degree 3, then 2(d/dx)(y^3.d^2y/dx^2) i...

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  16. If y=a t^2+2b t+c&t=a x^2+2b x+c , then (d^3y)/(dx^3) equals 24 a^2(a ...

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  17. Let f(x)=|cosxsinxcosxcos2xsin2x2cos2xcos3xsin3x3cos3x| then f'(pi/2)=...

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  18. people living at Mars ,instead of the usual definition of derivative D...

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  19. (lim)(xvec0^+)1/(xsqrt(x))("a t a n"^(-1)(sqrt(x))/a-btan^(-1)(sqrt(x)...

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  20. Let y=ln(1+cosx)^2 then the value of (d^2y)/(dx^2)+2/(e^(y//2)) equals...

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