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Show that the curves y=a^(x) and y=b^(x)...

Show that the curves `y=a^(x) and y=b^(x), a gt b gt 0` intersect at an angle of `tan^(-1) (|(log|(a)/(b)|)/(1+loga log b)|)`

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CBSE COMPLEMENTARY MATERIAL-APPLICATION OF DERIVATIVES-4 MARK QUESTIONS
  1. For the curve y=5x-2x^3 , if x increases at the rate of 2 units/sec, t...

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  2. Find the condition for the curve (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and...

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  3. Show that the curves y=a^(x) and y=b^(x), a gt b gt 0 intersect at an ...

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  4. Find the equation of the normal to the curve ay^(2)=x^(3) at the point...

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  5. Find the equation of the normal at a point on the curve x^(2)=4y, whic...

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  6. Find the point on the curve 9y^2=x^3, where the normal to the curve ma...

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  7. Show that the tangents to the curve y=2x^3-3 at the points where x=...

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  8. Using differentials, find the approximate value of (66)^(1//3)

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  9. sqrt(401)

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  10. Using differentials, find the approximate value of sqrt(0.037).

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  11. sqrt(25.3)

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  12. Using differentials, find the approximate value of (3. 968)^(3/2)

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  13. (26.57)^(1//3)

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  14. Find the value of log(10)(10.1) given that log(10) e=0.4343.

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  15. If the radius of a circle increases from 5 cm to 5.1 cm, find the incr...

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  16. If the side of a cube be increased by 0.1% find the corresponding incr...

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  17. Find the approximate value of f(2.01) where f(x) =x^(3)-4x+7.

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  18. Find approximate value of 1/(sqrt(25. 1)) using differentials.

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  19. The radius of a sphere shrinks from 10 to 9.8 cm. Find approximatel...

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  20. Find the maximum and minimum value of f(x)=sinx+1/2cos2xin[0,pi/2]dot

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