Use l'Hospital's Rule to find the exact value of the limit. 6* - 5* lim X-0 3x - 2x
Consider the following. lim 2x2 - 2x - 4 x-1 X + 1 Find the limit of the function (if it exists). (If an answer does not exist, enter DNE.) -6 Write a simpler function that agrees with the given function at all but one point. 9(x) =
if cos x = -and sin x > 0, find the exact value of sin(2x) VO and simplify
Dif equations 4
4. a) Determine whether the following differential equation is exact. (x + 2y) dx + (2x - y)dy = 0 b) Find the general solution using the method of exact differentials.
Question 11 5 pts Find exact value the limit, if it exists. If the limit does not exist, type "dne" and explain why. lim sin(x-2) x2-4 = x + 2
and << find the exact value of 4. If cos=- 4 a. sin e 6, tan 8 5. Prove the following identity. (sinx+cos x) =1+sin 2x 6. Ifcos(x)=5, and xc IV, find the exact value of each of the following. a.sin(2x) b.cos NI
3. Find the limit. lim X+0 (Inx)2 x (4 pts) exe-x-2x X-sin 4. Find the limit. lim * (4 pts)
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. 14 In x - 14 lim X - e Use l'Hôpital's Rule to rewrite the given limit so that it is not an indeterminate form lim 14 Inx-14 X-e = lim ( Evaluate the limit 14 Inx-14 lim =(Type an exact answer.)
Use L'Hospital to determine the following limit. Use exact values. In a lim > 1 31n z C Evaluate the limit using L'Hopital's rule lim 8 cos( – 3x)sec(5x)