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MHTCET 11 May 2024 Shift 1 Paper

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Question : 125 of 150

Marks: +1, -0

The approximate value of

(3.978)^{\frac{3}{2}}

is

7.934
8.934
7.022
8.866

Solution:

Concept:

Use linear approximation:

f(a+h) \approx f(a) + h f'(a)

.

Explanation:

Let

f(x) = x^{\frac{3}{2}}

.

Then

f'(x) = \frac{3}{2} x^{\frac{1}{2}}

.

Choose

a = 4

and

h = 3.978 - 4 = -0.022

.

Now,

f(4) = 4^{\frac{3}{2}} = 8

.

And

f'(4) = \frac{3}{2} \times 4^{\frac{1}{2}} = \frac{3}{2} \times 2 = 3

.

Using the approximation:

f(3.978) \approx f(4) + h f'(4)

= 8 + (-0.022)(3)

= 8 - 0.066 = 7.934

.

Answer:

The approximate value is

7.934

, which is option A.

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