Asked • 10/22/19

How do I solve these limit problems?

I need help solving these problems:

Let g and h be the functions defined by g(x)=−2x^2+4x+1 and h(x)=(1/2)x^2−x+(11/2). If f is a function that satisfies g(x) ≤ f(x) ≤ h(x) for all x, what is lim f(x) as x→1?

Let f, g, and h be the functions defined by f(x)=(sinx)/2x, g(x)=x^4 cos(1x/2), and h(x)=x^2/tanx for x≠0. All of the following inequalities are true on the interval [−1,1] for x≠0. Which of the inequalities can be used with the squeeze theorem to find the limit of the function as x approaches 0 ?

1- (1/4) ≤ f(x) ≤ x^2+(1/2)

2- −x^4 ≤ g(x) ≤ x^4

3- −(1/x^2) ≤ h(x) ≤ (1/x^2)

Let f, g, and h be the functions defined by f(x)= (1−cosx)/x^2, g(x)= x^2(sin(1/x)), and h(x)= (sinx)/x for x≠0. All of the following inequalities are true for x≠0. Which of the inequalities can be used with the squeeze theorem to find the limit of the function as x approaches 0 ?

1- (1/3)(1−x^2) ≤ f(x) ≤ (1/2)

2- −x^2 ≤ g(x) ≤ x^2

3- −(1/ |x|) ≤ h(x) ≤ (1/ |x|)

Which of the following limits are equal to −1 ?

1- lim as x→(0−) (|x| /x)

2- lim as x→3 (x^2−7x+12)/ 3−x

3- lim as x→∞ (1−x)/ 1+x 

1 Expert Answer

By:

Steven G. answered • 10/22/19

College Math Professor

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