Chapter 1: Q. 13 (page 135)

Suppose f and g are functions such that $\lim_{x \to 3} f (x) = 5, \lim_{x \to 4} f (x) = 2$ and $\lim_{x \to 3} g (x) = 4$
Given this information, calcuate the limits that follow, if possible. If it is not possible with the given information, explain why.
$\lim_{x \to 3} (2 f (x) - 3 g (x))$

Short Answer

Expert verified

The value of $\lim_{x \to 3} (2 f (x) - 3 g (x)) = - 2$

Step by step solution

Step 1. Given information

The given limits $\lim_{x \to 3} (2 f (x) - 3 g (x))$ and the given values are,

$\lim_{x \to 3} f (x) = 5, \lim_{x \to 4} f (x) = 2$ and $\lim_{x \to 3} g (x) = 4$

Step 2. Calculating value of the given limits

The value can be calculated as below,

$\lim_{x \to 3} (2 f (x) - 3 g (x)) = \lim_{x \to 3} (2 f (x)) - \lim_{x \to 3} (3 g (x)) [s u m r u l e] = 2 \lim_{x \to 3} f (x) - 3 \lim_{x \to 3} g (x) [c o n s \tan t m u l t i p l e r u l e] = 2 (5) - 3 (4) = 10 - 12 = - 2$

Hence,the result is $- 2$

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Suppose f and g are functions such that $\lim_{x \to 3} f (x) = 5, \lim_{x \to 4} f (x) = 2$ and $\lim_{x \to 3} g (x) = 4$
Given this information, calcuate the limits that follow, if possible. If it is not possible with the given information, explain why.
$\lim_{x \to 3} (2 f (x) - 3 g (x))$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating value of the given limits

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Suppose f and g are functions such thatlimx→3f(x)=5,limx→4f(x)=2andlimx→3g(x)=4Given this information, calcuate the limits that follow, if possible. If it is not possible with the given information, explain why.limx→32f(x)-3g(x)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating value of the given limits

One App. One Place for Learning.

Most popular questions from this chapter

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Suppose f and g are functions such that $\lim_{x \to 3} f (x) = 5, \lim_{x \to 4} f (x) = 2$ and $\lim_{x \to 3} g (x) = 4$
Given this information, calcuate the limits that follow, if possible. If it is not possible with the given information, explain why.
$\lim_{x \to 3} (2 f (x) - 3 g (x))$