4. (a) Either find the following limits or show that they don't exist. (i) \lim_{x \to 2} \frac{x^2 + 2x - 8}{x^2 - 5x + 6} (ii) \lim_{x \to \infty} (\sqrt{25x^2 + 2x} - 5x). (iii) \lim_{x \to 0} \frac{\tan(6x)\cos(5x)}{\sin(7x)}
Added by Kristina H.
Close
Step 1
To find this limit, we can first try to factor the numerator and denominator to see if there is a common factor that can be canceled out. Numerator: x^2 + 2x - 8 = (x - 2)(x + 4) Denominator: x^2 - 5x + 6 = (x - 2)(x - 3) Now, we can cancel out the common Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 80 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
(b) Find each of the following limits. (If an answer does not exist, enter DNE.) (i) lim sgn x x->0+ (iii) lim sgn x x->0 DNE (iv) lim |sgn x| x->0 DNE
Adi S.
Find each of the following limits, or show that the limit does not exist. An answer of only does not exist is not sufficient and should be explained. For infinite limits, state whether the limit approaches positive or negative infinity. a) lim x→0 (√(25+16x²)-5)/(2x²) b) lim x→4⁺ √(x)/(8-2x) c) lim x→0 (1/2x - 3/(x²+6x)) d) lim x→∞ (6x¹²(5x+3)²)/(2+15x⁴) e) lim x→-∞ (16arctan(5x)+14π)/(4arctan(9x)+5π) f) lim x→∞ (x+7)⁵(3-x)⁹
Find the indicated limit or show that it does not exist using the following facts about limits involving the functions f(x) and g(x): lim f(x) = -5, lim g(x) = -3, lim f(x) = 9, and lim g(x) = 1. lim [4f(x) + 2g(x)] as x approaches 16.
Trent S.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD