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Application of Derivatives

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Long Answer Type

351.

Find the largest possible area of a right-angled triangle whose hypotenuse is 5 cm long.

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352. A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is

open parentheses straight a to the power of 2 over 3 end exponent plus straight b to the power of 2 over 3 end exponent close parentheses to the power of 3 over 2 end exponent.

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353. Find the maximum-area of an isosceles triangle inscribed in the ellipse

straight x squared over straight a squared plus straight y squared over straight b squared space equals space 1

with its vertex at one end of the major axis.

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Short Answer Type

354.

Let AP and BQ be two vertical poles at points A and B, respectively. If AP = 16 m. BQ = 22 m and AB = 20 m, then find the distance of a point R on AB from the point A such that RP² + RQ² is minimum.

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Long Answer Type

355.

If length of three sides of a trapezium other than base are equal to 10 cm. then find the area of the trapezium when it is maximum.

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Short Answer Type

356.

Use differentials to approximate $square root of 25.3 end root.$

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357.

Use differentials to approximate $square root of 0.037 end root$ .

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358.

Use differentials to approximate $square root of 36.6 end root$

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359.
Use differentials to approximate:
$square root of 49.5 end root$

Take

straight y space equals space square root of straight x comma space space space space space straight x space equals space 49 comma space space space space space dx space equals space δx space equals space 0.5 space space space so space tha space straight x plus δx space equals space 49.5

Now,

space space space space straight y plus δy space equals space space square root of straight x plus δx end root space space space space space space space space space space space space space rightwards double arrow space space space δy space equals space square root of straight x plus δx end root space minus space straight y space equals space square root of 49.5 end root space minus space 7

rightwards double arrow

square root of 49.5 end root space equals space space δy space plus space 7

...(1)
Now,

δy

is approximately equal to dy
and

dy space equals space dy over dx dx space equals space fraction numerator 1 over denominator 2 square root of straight x end fraction dx space equals space fraction numerator 1 over denominator 2 square root of 49 end fraction left parenthesis 0.5 right parenthesis space equals space fraction numerator 0.5 over denominator 14 end fraction space equals space 0.0357

therefore space space space space from space left parenthesis 1 right parenthesis comma space space space space square root of 49.5 end root space equals space 0.0357 space plus space space 7 space equals space 7.0357

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360.

Use differentials to approximate:
$square root of 0.6 end root$

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Previous Year Papers

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Long Answer Type

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Long Answer Type

Short Answer Type

359. Use differentials to approximate:

359.
Use differentials to approximate:
$square root of 49.5 end root$