5. If f is differentiable at a, where a > 0, evaluate the following limit in terms of f'(a): lim f(x) - f(a) √x- ſa
Question 4): If f(x) is differentiable at a, where a > 0, evaluate the following limit in terms of f'(a): lim ") – f(a)
1 Given lim f(x) = 5, lim g(x) = -2, and lim h(x) = 0, evaluate the limit: lim x-c f(x) - 8(x) 1-C X- X-C 1 5 b) c) d) e) does not exist
• Question 8 Evaluate the limit: lim h 0 (3 + h)2 – 9 h • Question 9 α Evaluate the limit: lim 1 +9 15x + 54 2 - 9
Evaluate the limit lim x→5 x^2 −2x−15/ x^2 −25 Evaluate the limit lim x→∞ x^2 + x /x^5 c. Find all points on the graph of f(x) = 2x^3 −x where the tangent line is parallel to the line y = 149x + 7.
definition of limit to prove that lim ,-e3. 3, (a) Use the - (b) Suppose lim g(z) 0 and if(x)| |g(z)| for all z E R. Use the ε-δ definition of limit to prove that lim f(x)=0 definition of limit to prove that lim ,-e3. 3, (a) Use the - (b) Suppose lim g(z) 0 and if(x)| |g(z)| for all z E R. Use the ε-δ definition of limit to prove that lim f(x)=0
Evaluate the following limit using Taylor series. -X- In (1 - x) lim x→0 106² - x - In (1 – X) lim (Simplify your answer.) x→0 1082
4. Evaluate the limit (4pts each) 9x4+x (a) lim x -3 (b) lim Vx +25 4. Evaluate the limit (4pts each) 9x4+x (a) lim x -3 (b) lim Vx +25
Thank you. - Part 1: Limit of a difference quotient Suppose f(x) = – 5. Evaluate the limit by using algebra to simplify the difference quotient (in first answer box) and then evaluating the limit (in the second answer box). X - 2 (f(5 + h) – f(5) lim h0 Him ( 15 + ) - 109 ) = lim ( = lim h0 | Part 2: Interpreting the limit of a difference quotient - Part 1: The derivative at...
2. Evaluate lim ? (Do NOT use a table or a graph to evaluate the limit.) [6 pts]