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Let f(x)=xsinpix ,\ x >0 . Then for ...

Let `f(x)=xsinpix ,\ x >0` . Then for all natural numbers `n ,\ f^(prime)(x)` vanishes at (a) A unique point in the interval `(n ,\ n+1/2)` (b) a unique point in the interval `(n+1/2,\ n+1)` (c) a unique point in the interval `(n ,\ n+1)` (d) two points in the interval `(n ,\ n+1)`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
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  2. Find (dy)/(dx) if y=sec^(-1)((sqrt(x)+1)/(sqrt(x)-1))+sin^(-1)((sqrt(x...

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  3. Let f(x)=xsinpix ,\ x >0 . Then for all natural numbers n ,\ f^(pr...

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  4. Find (dy)/(dx) if y=tan^(-1)((4x)/(1+5x^2))+tan^(-1)((2+3x)/(3-2x))

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  5. If y=sec^(-1)(1/(2x^2-1));0ltxlt (sqrt(2)), then find= (dy)/(dx)

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

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  7. Find (dy)/(dx) if y=log{e^x((x-2)/(x+2))^(3/4)}

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  8. let f(x)=2+cosx for all real x. Statement 1: For each real t, there e...

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

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

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  11. Differentiate the following functions with respect to x from first...

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  12. If f(x) is differentiable and strictly increasing function, then the v...

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  13. If f(x)=[2x]sin3pix then prove that f'(k^(+))=6kpi(-1)^(k), (where [.]...

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  14. lim(h->0) (f(2h+2+h^2)-f(2))/(f(h-h^2+1)-f(1)) given that f'(2)=6 and ...

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  15. Evaluate lim(h->0)((a+h)^2sin^(-1)(a+h)-a^2sin^(-1)a)/h

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  16. If x^2+y^2=1, then (a)y y^('')-2(y^(prime))^2+1=0 (b)yy^('')+(y...

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  17. Using the first principle, prove that d/(dx)(1-x^2)=-2x

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  18. If y is function of x and log(x+y)=2xy, then find the value of y'(0).

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  19. Find the derivative of sqrt(4-x) w.r.t. x using the first principle.

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  20. The slope of the tangent to the curve (y-x^5)^2=x(1+x^2)^2 at the poin...

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