APPROXIMATION

APPROXIMATION VALUE 

 by DIFFERENTIATION

1)
Using the method of differential, find the approximation value of

a) √25.02                  b) ³√0.009

c) ⁴√627                   

e) sin 61º, given that 1º = 0.01745

f) cos 11π/24, given π=3.14159

g) log₁₀40.05,given log₄=0.6021 and log₁₀e = 0.4343

h) logₑ(25.02) given logₑ=3.2189

i) tan 44º given 1º =0.01745

2) The radius of a balloon is 7cm. If an error of 0.01cm. is made in measuring the radius. find the error in measuring the volume of the balloon.

3) A closed circular cylinder has height 16cm. and radius r cm. The tital surface areas is A cm². Prove that dA/dr = 4π(r+8). 
Hence calculate an approximate increase in area if the radius increases from 4 to 4.02cm, the height remaining constant.

4) The area of two circles of radii 7cm and 7.02cm.

5) The volume of two spheres of radii 10cm and 9.99cm.

6) The radius of a sphere is found by  measurement to be 10cm. if there be a maximum probable error of 0.05cm. in the measurement of the radius, find the maximum possible error in the computation of the surface area of the sphere.

6) Due to heating the side if a metalic cube expands from 4 to 4.05cm. find the approximately the increase in volume of the cube.

7) If there is an error of 1% in measuring the radius of a sphere, what is the approximate percentage error in the measurement of the volume of the sphere.