Prove that the function as x → 1 are infinitesimal
My Self Assessment
Find
a) 0
b) 1
c) sin1°
d) ∞
Making use of method of replacing an infinitesimal with an equivalent one, find the following limit
c) −2
d) 2
Find approximate value of the root
a) 10
b) 10.14
c) 10.18
d) 10.21
Let be an interior angle of a regular n–gon (n = 3, 4, 5,. . .). Write the first several terms of the sequence . Prove that .
Prove that at any arbitrary chosen x, the sequence is bounded. [x] denotes the greatest integer ≤ x
Prove that the sequence has limit as n → ∞ where [x] is the largest integer ≤ x
Given the function f
Prove that .
Find the constants a and b from the condition
a) a = b = 0
b) a = 1, b = − 1
c) a = b = 1
d) a = b = −1
Find the derivative of the following function
Show that the function satisfies the differential equation xy' = (1 − x2) y.
Show that the function y = satisfies the equation
.
If show that
Show that the function satisfies the differential equation
Find the derivative of the function
Find the derivative of the nth order of the function y = lnx
a)
b)
c)
d)
Find the derivative of the nth order of the function y =