Q. 36

Question

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.

$\lim_{x \to 3} x^{4} .$

Step-by-Step Solution

Verified

Answer

The limit exists and it is equal to 81.

1Step 1. Given Information.

$G i v e n : \lim_{x \to 3} x^{4}$

2Step 2. Theorem 1.16

$P o w e r f u n c t i o n s a r e c o n t i n u o u s o n t h e i r d o m a i n s . I n t e r m s o f l i m i t s, i f A i s r e a l a n d k i s r a t i o n a l, t h e n f o r a l l v a l u e s x = c a t w h i c h x^{k} i s d e f i n e d w e h a v e \lim_{x \to c} A x^{k} = A c^{k} .$

3Step 3. Finding limit of given function.

$U \sin g t h e a b o v e t h e o r e m, A = 1, c = 3 a n d k = 4 . S o, p u t t i n g t h e s e v a l u e s w e g e t o u r l i m i t a s : \lim_{x \to 3} x^{4} = 3^{4} = 81 .$

Q. 35

Q. 37

Other exercises in this chapter

Q. 34

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.limx→-1 x.

View solution

Q. 35

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.limx→-5 (3x-2)

View solution

Q. 37

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.limx→0 x-3 .

View solution

Q. 38

For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.limx→-5 x .

View solution