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USHA PUBLICATION-CONTINUITY AND DIFFERENTIABILITY APPLICATION OF DERIVATIVES -EXERCISE
- If ysqrt(x^2 +1) = log{sqrt(x^2 +1)- x} then prove that (x^2 +1) dy/dx...
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- If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a
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- Write the subinterval of (0,pi) in which sin (x+pi/4) is increasing.
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- Find the intervals where the following functions are (a) increasing an...
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- Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...
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- Find the points on the curve x^2+y^2-2x-4y+1=0,where the tangent is pa...
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- Find the equations of the tangent and the normal to the curve y = (x-7...
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- Find the angle of intersection of two curves y =2^x and y=5^x
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- Show that x/(1+ x tan x,) x in (0,pi/2)is maximum when x = cos x.
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- Show that f(x)=(logx)/xhas minimum value at x=e
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- Find (dy)/(dx) if x=(3at)/(1+t^3), y=(3at^2)/(1+t^3) at t=1/2
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- Find the extreme values of the function f(x)=x^2e^(-x^2) and show that...
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- A curve passes through the point (2, 0) and slope of tthe tangent at a...
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- A figure consists of a semi-circle with a rectangle on its diameter. G...
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- what is the direction of cosine of the line passing through (4,2,3) an...
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- Show that the line y=mx+c touches the curve x^2/a^2-y^2/b^2 = 1 if c^2...
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- Find the equation of the tangent and normal to the curve y(x-2)(x-3)-x...
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- Find (dy)/(dx) if y=(1)/(sqrt(a^(2)-x^(2)))
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- Find (dy)/(dx) if y=((5x-1)^(2/3)(2x-5)^(3/5))/((x-1)^(1/3)(3x-2)^3)
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- If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y) , then prove that (dy)/(dx)=sqrt...
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