4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c) 4. Find the following limits by using L'Hôpital's rule. 1 +...
Evaluate the following limits using l'Hôpital's Rule 10. lim sinx-2 x 7x3 10. lime sinti? 11. lim (1-3)* 12. lime e2-1 + 2x 12. lim 24-+2x 0
Question 4. Determine (if they exist) the following limits (using l'Hôpital's rule): In(1 + r) - 3 (a) lim (6) (1+r)-1 lim 22 (PER). 10 10 Verify that the assumptions of the theorem on l'Hôpital's rule are satisfied.
Evaluate the following limit using l'Hôpital's Rule. 7In x-7 lim X-e Xe Use l'Hôpital's Rule to rewrite the given limit so that it is not an indeterminate form. 7in x-7 lim X-e = lim Xe Xe Evaluate the limit. 7In x-7 7 = (Type an integer or a fraction.) lim X-e X-e n. Find the solution of the following initial value problem. p' (t) = 65 e -; (O) = 280 The solution of the initial value problem is p(t)...
question c TOPIC 2: Trig Limits TRIG LIMITS: If direct substitution doesn't work, most triglimits can be solved by expressing the limit as a product of these special trig limits. 1. so also Lim 1 0 sinx |-cosx cos X-1 Lim - 0, so Lim =0, BUT Lim so useless! 01-Cos 0 Limsin 0 SQUEEZE THEOREM is covered and used for some proofs in the teaching videos, but will not be tested Q.14 Please evaluate the following limits, without using...
-0. (incorrect) 8. (1 point) Compute the following limits using l'Hôpital's rule if appropriate. Use INF to denote oo and MINF to denote 1 - cos(8x) lim x+01 – cos(7x) 8x – 7* – 1 lim x² - 1 Answer(s) submitted: toy (incorrect) 9. (1 point) Compute the following limit using l’Hôpital's rule if appropriate. Use INF to denote oo and MINF to denote -0. lim 7 sin(x) ln(x) = x ot Answer(s) submitted:
Evaluate the limit, using L'Hôpital's Rule if necessary. x3 lim X-00 9eX/5 Step 1 +3 The limit to be evaluated is lim ** 9ex/5 By direct substitution we have the following. *3 lim x 9ex/5 Thus, the direct substitution results in --Select-- form. Submit Skip (you cannot come back)
5. (8 points each) Find the limits: V3x2-6 (a) lim X-00 2x -9X (b) lim x=0x2-sinx COS X (c) lim x X- 2 2
Q3. Find the following limits: x1 x+1 (b) lim (c) lim X-3 X-2
#2 1. (8 points) Evaluate the limit, without using L'Hôpital's Rule: x² – 2x - 3 lim 2+3 22 – 5x + 6 Note that 3 is a zero of the denominator polynomial, so you need to use the technique of Example 4.2.5(d) p. 113. 2. (8 points) In the previous problem, can L'Hôpital's Rule be applied? If so, evaluate the limit using L'Hôpital's Rule; if not, indicate how the limit expression does not satisfy the conditions required for L'Hôpital's...
Determine the exact value of the following limits using L'Hôpital's Rule where possible.