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(a) lim x→3 √x + 6 − x x3− 3x2

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(1)

1. hw 7 Deadline: 11/11 (5pm)

(1) Read Section 2.2, 2.3, 2.4 of the book by Stewart.

(2) Do Exercise 1, 22, 27 on page 102-103 (Section 2.3) (3) Do exercise 28, 29 on page 114 (Section 2.4.).

(4) Use definition to prove that lim

x→2

√ x

x2+ 5 = 2 3. (5) Find the value a such that lim

x→0

√3

ax + 8 − 2

x = 5

12. (6) Let p(x) = x6+ 2x5− x + 1. Evaluate lim

x→∞(p6

p(x) − x).

(7) Evaluate the limits.

(a) lim

x→3

√x + 6 − x x3− 3x2 . (b) lim

x→0

(1 + x)(1 + 2x)(1 + 3x) − 1

x .

(c) lim

x→1

x10− 1 x99− 1. (d) lim

x→2

(x10− 210) − 10 · 29(x − 2)

(x − 2)2 .

(e) lim

x→1

 m

1 − xm− n 1 − xn



where m, n are distinct natural numbers.

(f) lim

x→−2

√3

x − 6 + 2 x3+ 8 . (g) lim

x→1

m√ x − 1

√n

x − 1, where m, n are natural numbers.

(h) lim

x→1

(1 −√

x)(1 −√3

x) · · · (1 −√n x) (1 − x)n−1 . (i) lim

x→a

√x −√ a +√

x − a

√x2− a2 . Here a > 0.

1

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