(a) lim sin )(b) Suppose f (x) is defined on (-∞, 0), that g (x) =and f (x) = g (x) if x # 4. Find lim ƒ (x).x²–16x-4if x # 4sin(x-3)(c) If it is given that limI-31, then compute5 sin(r-3) + x²x-3limx→3

In all 3 we need to find the limit of given function.

(a) lim sin (n (b) Suppose f (x) is defined on (-0, 0), that g (x) = if x + 4 and f (x) = g (x) if x # 4. Find lim f (x). x-4 x→4 (c) If it is given that lim sin(x-3) = 1, then compute x-3 6. X→3 5sin(x-3) + x² lim x-3 x→3

(a) lim sin (n (b) Suppose f (x) is defined on (-0, 0), that g (x) = if x + 4 and f (x) = g (x) if x # 4. Find lim f (x). x-4 x→4 (c) If it is given that lim sin(x-3) = 1, then compute x-3 6. X→3 5sin(x-3) + x² lim x-3 x→3

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 8E

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

(a) lim sin )
(b) Suppose f (x) is defined on (-∞, 0), that g (x) =
and f (x) = g (x) if x # 4. Find lim ƒ (x).
x²–16
x-4
if x # 4
sin(x-3)
(c) If it is given that lim
I-3
1, then compute
5 sin(r-3) + x²
x-3
lim
x→3

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