Question

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number (a).

f(x) = (x+3x⁵)⁴ , a = -1

Answer 1

To show that the function f(x)=(x+3x⁵)⁴ is continuous at x=-1, you need to show that the limit of the function as x approaches -1 exists and is equal to the value of the function at x=-1.

Step-by-step explanation:

To show that the function f(x)=(x+3x⁵¹ⁱ)⁴ is continuous at x=-1, we need to show that the limit of the function as x approaches -1 exists and is equal to the value of the function at x=-1.

First, let's find the limit of f(x) as x approaches -1.

lim(x->-1) (x+3x⁵¹ⁱ)⁴ = (-1+3(-1)⁵¹ⁱ)⁴ = (-1-3)⁴ = -4⁴ = 256

Next, let's find the value of f(x) at x=-1.

f(-1) = (-1+3(-1)⁵¹ⁱ)⁴ = (-1-3)⁴ = -4⁴ = 256

Since the limit and the value of the function at x=-1 are both equal to 256, we can conclude that the function f(x)=(x+3x⁵¹ⁱ)⁴ is continuous at x=-1.