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UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
- Prove that: underset(xrarrpi/2)lim (1+cosx)^(3secx) = e^3
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- Prove that: underset(xrarr0)lim ([1+3x]^((x+3)/x))= e^9
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- Evaluate the following limits: underset(x rarr0)lim(xe^x - log(x+1))/(...
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- Evaluate the following limits: underset(x rarr0)lim[tan(pi/4+x)]^(1/x)
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- Evaluate the following limits: underset(x rarr0)lim(sinx + cos x)^(1/x...
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- Evaluate the following limits: underset(x rarr0)limsinlog(1+x)/log(sin...
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- It g(x) is the inverse of f(x) and f(X) = (1+x^3)^-1, show that g'(x) ...
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- Find the differential coefficients of the folloiwng functions: x^x
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- Find form 1st principle the differential coefficients of the folloiwng...
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- Find form 1st principle the differential coefficients of the folloiwng...
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- Find dy/dx when x^(siny) + y ^(sinx) = 1
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- Find dy/dx when x^(logx) + (sinx)^x + 15 x
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- Find (d^2y)/(dx^2) when x= e^-t and y = te^-1
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- Find (d^2y)/(dx^2) when x= a sin^3t and y = a cos^3 t at t = pi/4
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- Find (d^2y)/(dx^2) when x=a(t-sint) and y = a (1+cost) at t = pi/...
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- If y^2 (1-x^2) = x^2 +1, show that (1-x^4) (dy/dx)^2 = y^4 -1.
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- If x = sec theta - cos theta, y = sec^n theta - cos^n theta, then show...
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- If y= x^(y^x), prove that y1 = (ylogy(1+x logx logy)/(x log x (1-xlogy...
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- or,find the derivatives of tan^(-1) ((sqrt(1+x^2)-1)/x) with respect t...
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- If y = (Sin ^-1 x)^2 + (cos^-1 x)^2, then show that (1-x^2) y 2 - xy1 ...
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