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If x=acostheta,y=bsintheta, then prove t...

If `x=acostheta,y=bsintheta,` then prove that `(d^3y)/(dx^3)= -(3b)/(a^3)cos e c^4thetacotthetadot`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Find (dy)/(dx) for the function: y=sin 4x - (1/x^4)

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  2. Find (dy)/(dx) for the function: y=sin 2x - x^4 + e^(-3x)

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  3. If x=acostheta,y=bsintheta, then prove that (d^3y)/(dx^3)= -(3b)/(a^3)...

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  4. If y=xlog"{"x/((a+b x))"}" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...

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  5. A function f: R->R satisfies the equation f(x+y)=f(x)f(y) for all...

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  6. If u=x^2+y^2 and x=s+3t, y=2s-t, then (d^2u)/(ds^2) is (a) 5/2 t (b) ...

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  7. If f(x)=(1+x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+...

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  8. If f(x)=sinx+e^x , then f''(x)

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  9. "If "y^(2)=ax^(2)+bx+c," then "y^(3)(d^(2)y)/(dx^(2)) is

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  10. If f(x)=|x^nn !2cosxcos(npi)/2 4sinxsin(npi)/2 8| then find the val...

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  11. Let f((x+y)/(2))= (f(x)+f(y))/(2) for all real x and y. If f'(0) exits...

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  12. If y^(1/m)=(x+sqrt(1+x^2)),t h e n(1+x^2)y2+x y1 is (where yr repres...

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  13. Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...

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  14. f(x)+f(y)=f((x+y)/(1-xy)) ,for allx,yinR.(xy!=1),and lim(x->0) f(x)/x=...

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  15. Let f: R->R satisfying |f(x)|lt=x^2,AAx in R be differentiable at x...

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  16. If f(x)=sin^(-1)cosx , then the value of f(10)+f^(prime)(10) is (a)11-...

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  17. If (sinx)(cosy)=1/2, then (d^2y)/(dx^2) at (pi/4,pi/4) is (a) -4 (b) -...

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  18. Suppose p(x) = a0 + a1x + a2x^2 +…+ anx^n. If |p(x)| le |e^(x-1) - 1| ...

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  19. Let f(x+y)=f(x)dotf(y) for all xa n dydot Suppose f(5)=2a n df^(prime)...

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  20. A function f satisfies the condition f(x)=f^(prime)(x)+f''(x)+f'''(x)....

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