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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
- If '' (x)=-f(x) and g(x)=-f'(x) and F(x)=(f(x/2))^2 + (g(x/2))^2 and ...
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- Find (dy)/(dx) for the function: y=sin 4x - (1/x^4)
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- Find (dy)/(dx) for the function: y=sin 2x - x^4 + e^(-3x)
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- If x=acostheta,y=bsintheta, then prove that (d^3y)/(dx^3)= -(3b)/(a^3)...
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- If y=xlog"{"x/((a+b x))"}" , then show that x^3(d^2y)/(dx^2)=(x(dy)/(d...
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- A function f: R->R satisfies the equation f(x+y)=f(x)f(y) for all...
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- 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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- If f(x)=(1+x)^n, then the value of f(0)+f^(prime)(0)+(f^('')(0))/(2!)+...
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- If f(x)=sinx+e^x , then f''(x)
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- "If "y^(2)=ax^(2)+bx+c," then "y^(3)(d^(2)y)/(dx^(2)) is
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- If f(x)=|x^nn !2cosxcos(npi)/2 4sinxsin(npi)/2 8| then find the val...
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- Let f((x+y)/(2))= (f(x)+f(y))/(2) for all real x and y. If f'(0) exits...
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- 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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- Suppose the function f(x)-f(2x) has the derivative 5 at x=1 and deriva...
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- 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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- Let f: R->R satisfying |f(x)|lt=x^2,AAx in R be differentiable at x...
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- If f(x)=sin^(-1)cosx , then the value of f(10)+f^(prime)(10) is (a)11-...
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- If (sinx)(cosy)=1/2, then (d^2y)/(dx^2) at (pi/4,pi/4) is (a) -4 (b) -...
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- Suppose p(x) = a0 + a1x + a2x^2 +…+ anx^n. If |p(x)| le |e^(x-1) - 1| ...
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- Let f(x+y)=f(x)dotf(y) for all xa n dydot Suppose f(5)=2a n df^(prime)...
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