Real Analysis Answers

Separate the interval in which the function f defined on R by f(x)=2x3-15x2+36x+5 for all x∈R is increasing

Using weiestrass M-test, show that the following series converges uniformly.

∞

∑n^3X^n,X belongs to[-1/3,1/3]

n=1

Using the definition, show' that the sequence [1/√n]neN is Cauchy.

Use the substitution theorem evaluate,

Integral 0 to 2 t^2[1+t^3]^-1/2dt

Apply second substitution theorem evaluate

Integral 1 to 4 dt/(|t+4|√t)

If f and g are continuous functions on [a,b] with integral from a to x f ≥ integral from a to x g for every x ∈ [a, b], must it be true that f(x) ≥ g(x) on [a, b]?

Apply second substitution theorem evaluate

i) integral 1 to 9 (√ t)/(2+√t)

Find the relative extrema for

i) 𝑓( 𝑥 )= 𝑥^3 − 3𝑥 + 5

𝑖𝑖) f(x)=𝑥^4 + 2𝑥^2 − 4