Q. 64.0( 4 Votes )

# Find the approximate value of (1.999)^{5}.

Answer :

Given (1.999)^{5}

But the integer nearest to 1.999 is 2,

So, 1.999 = 2-0.001

∴, a = 2 and h = -0.001

Hence, (1.999)^{5} = (2+(-0.001))^{5}

Let the function becomes,

f(x) = x^{5}………(i)

Now applying first derivative, we get

f’(x) = 5x^{4}……….(ii)

Now let f(a+h) = (1.999)^{5}

Now we know,

f(a+h) = f(a)+hf’(a)

Now substituting the function from (i) and (ii), we get

f(a+h) = a^{5}+h(5a^{4})

Substituting the values of a and h, we get

f(2+(-0.001)) = 2^{5}+( -0.001) (5(2^{4}))

⇒ f(1.999) = 32+(-0.001)(5(16))

⇒ (1.999)^{5} = 32+(-0.001)(80)

⇒ (1.999)^{5} = 32-0.08

⇒ (1.999)^{5} = 31.92

Hence the approximate value of (1.999)^{5} = 31.92.

Rate this question :

If y = sin x and x changes from to, what is the approximate change in y?

RD Sharma - Volume 1Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of the edges of the cube.

RD Sharma - Volume 1The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume.

RD Sharma - Volume 1