Errors and Approximations MCQ Quiz in বাংলা - Objective Question with Answer for Errors and Approximations - বিনামূল্যে ডাউনলোড করুন [PDF]

Concept:

If an expression is A = 

The error per cent of A , =  +  + . 

Calculation:

Given arm length of the cube is 10 cm.

The error in the length of the arm is 0.08 cm.

⇒ Δ L = 0.08

∴  = 0.008.

We know that the volume of the cube is given by V = l³.

⇒ V = 10³ = 1000 cm³

Error in the volume is given by:

⇒ 

⇒  = 3 × 0.008

⇒  = 0.024

⇒ Δ V = V × 0.024

⇒ Δ V = 1000 × 0.024

⇒ Δ V = 24

The approximate error in the volume of the cube is 24 cm³.

Concept: 

Let small charge in x be Δx and the corresponding change in y is Δy.

Therefore 

Calculation:

We have to find the value of 

Let x + Δx = 242 = 243 - 1

Therefore, x = 243 and Δx = - 1

Assume,           

Differentiating with respect to x, we get

At x = 243

 and y = 

As we know 

So, 

Therefore, approximate value of  = y + Δy = 3 - 0.0024 = 2.997

Concept: 

Let small change in x be Δx and the corresponding change in y is Δy.

Therefore 

Calculation:

We have to find the value of 

Let x + Δx = 36.01 = 36 + 0.01

Therefore, x = 36 and Δx = -0.01

Assume,           

Differentiating with respect to x, we get

At x = 36

 and y = 

As we know 

So, 

Therefore, approximate value of  = y + Δy = 6 + 0.00083 = 6.00083