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BANSAL-LIMITS AND DERIVATIVES-All Questions
- Evaluate ("Lim")(x->0)(logcosx)/x using Lhospitals Rule
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- Evaluate ("Lim")(x->0)(2^x-1)/((1+x)^(1//2)-1) using Lhospitals Rule
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- Evaluate ("Lim")(x->pi/4)(2-tanx)^(1/(ln(tanx))) using Lhospitals Rule
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- If ("Lim")(x->a)(a^x-x^a)/(x^x-a^a)=-1 and a >0 , then find the value ...
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- f(x)=(1n(x^2+e^x))/(1n(x^4+e^(2x)))dotT h e n lim(x->oo)f(x) is equal...
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- Let f(x+y)=f(x)f(y) for all x and y . Suppose f(5)=2 and f^(prime)(0)=...
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- Let f(x y)=f(x)f(y)\ AA\ x ,\ y in R and f is differentiable at x=1 s...
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- 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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- If f is twice differentiable such that f^(x)=-f(x) and f^(prime)(x)=g(...
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- Let f(x)=(lim)(h->0)(("sin"(x+h))^(1n(x+h))-(sinx)^(1nx))/hdot Then f...
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- Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f"(x)-2f'(x)-15f(...
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- Let u(x) and v(x) are differentiable functions such that (u(x))/(v(x))...
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- A function is represented parametrically by the equations x=(1+t)/(...
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- If x=t^3+t+5 & y=sint then (d^2y)/(dx^2)= (a) -((3t^2+1)sint+6tcost)/(...
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- Let g is the inverse function of fa n df^(prime)(x)=(x^(10))/((1+x^2))...
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- The equation y^2e^(x y)=9e^(-3) x^2 defines y as a differentiable func...
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- A nonzero polynomial with real coefficient has the property that f(x)=...
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- 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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- (lim)(hvec0)((e+h)^(1n(e+h))-e)/hi s
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- For the curve represented implicitly as 3^x-2^y=1 , the value of ("Lim...
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