To solve this limit, we can use the limit properties and the binomial theorem.

The binomial theorem states that (a + b)^n = a^n + n*a^(n-1)*b + ... + b^n.

So, (3 + h)^3 = 3^3 + 3^2*3h + 3*3^2*h^2 + h^3 = 27 + 27h + 27h^2 + h^3.

Therefore, the expression (3 + h)^3 - 27h becomes 27 + 27h + 27h^2 + h^3 - 27h = 27 + 27h^2 + h^3.

Now, we can take the limit as h approaches 0: lim h→0 (27 + 27h^2 + h^3).

Since h is approaching 0, h^2 and h^3 will also approach 0. Therefore, the limit is 27.

Question

To solve this limit, we can use the limit properties and the binomial theorem.

The binomial theorem states that (a + b)^n = a^n + n*a^(n-1)*b + ... + b^n.

So, (3 + h)^3 = 3^3 + 3^2*3h + 3*3^2*h^2 + h^3 = 27 + 27h + 27h^2 + h^3.

Therefore, the expression (3 + h)^3 - 27h becomes 27 + 27h + 27h^2 + h^3 - 27h = 27 + 27h^2 + h^3.

Now, we can take the limit as h approaches 0: lim h→0 (27 + 27h^2 + h^3).

Since h is approaching 0, h^2 and h^3 will also approach 0. Therefore, the limit is 27.

Knowee AI · Accepted Answer

To solve this limit, we can use the limit properties and the binomial theorem.

The binomial theorem states that (a + b)^n = a^n + n*a^(n-1)*b + ... + b^n.

So, (3 + h)^3 = 3^3 + 3^2*3h + 3*3^2*h^2 + h^3 = 27 + 27h + 27h^2 + h^3.

Therefore, the expression (3 + h)^3 - 27h becomes 27 + 27h + 27h^2 + h^3 - 27h = 27 + 27h^2 + h^3.

Now, we can take the limit as h approaches 0: lim h→0 (27 + 27h^2 + h^3).

Since h is approaching 0, h^2 and h^3 will also approach 0. Therefore, the limit is 27.

Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)lim h→0 (3 + h)3 − 27h