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Prove that the tangent drawn at any poin...

Prove that the tangent drawn at any point to the curve `f(x)=x^5+3x^3+4x+8` would make an acute angle with the x-axis.

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CENGAGE ENGLISH-APPLICATION OF DERIVATIVES-ILLUSTRATION
  1. Find the total number of parallel tangents of f1(x)=x^2-x+1a n df2(x)=...

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  2. Prove that the tangent drawn at any point to the curve f(x)=x^5+3x^3+4...

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  3. Find the equation of tangent to the curve y=sin^(-1)(2x)/(1+x^2)a tx=s...

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  4. The equation of the tangent tothe curve y={x^2 sin(1/x),x!=0 and 0, x...

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  5. Find the equation of normal line to the curve y=x^3+2x+6 which is para...

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  6. If the equation of the tangent to the curve y^2=a x^3+b at point (2,3)...

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  7. For the curve y=4x^3-2x^5, find all the points at which the tangents p...

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  8. Find the equation of tangent to the curve reprsented parametrically by...

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  9. For the curve x y=c , prove that the portion of the tangent intercepte...

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  10. If the tangent at any point (4m^2,8m^2) of x^3-y^2=0 is a normal to th...

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  11. Find all the tangents to the curve y=cos(x+y),-2pilt=xlt=2pi that are ...

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  12. Find the equation of all possible normals to the parabola x^2=4y drawn...

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  13. Find the equations of the tangents drawn to the curve y^2-2x^3-4y+8...

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  14. From the point (1,1) tangents are drawn to the curve represented param...

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  15. Show that the straight line xcosalpha=p touches the curve x y=a^2, if ...

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  16. Find the condition that the line A x+B y=1 may be normal to the curve ...

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  17. Find the acute angle between the curves y=|xhat2-1|a n d y=|x^2-3| at ...

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  18. Find the angle between the curves 2y^2=x^3a n dy^2=32 xdot

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  19. Find the cosine of the angle of intersection of curves f(x)=2^x(log)e ...

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  20. Find the angle between the curves y^(2)=4xand y=e^(-x//2).

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