3. Use algebra, limit laws and/or Standard Limits for sequences to evaluate the following expression. You...
Consider the limit lim V5x2 – x + 2 - (x – 7) X-00 5x2-x+2+(x-7) (a) By multiplying the expression inside the limit by V5x2-x+2+(x-7) and simplifying, write the limit as an indefinite form (b) Use algebra and limit laws to evaluate the indefinite form found in (a). Do not use L'Hopital's rule to do this. You do not have to state explicitly which limit law(s) you are using.
Question 2 (10 marks) In this question you must state if you use any standard limits, continuity, l'Hôpital's rule, the sandwich theorem or any convergence tests for series. You do not need to justify using limit laws 2n n3 or explain why it does not exist. (a) Evaluate lim n (b) Determine whether each of the following converge: n+3 2n (i) 2 (3n) (ii) (n3)! n=1 Question 2 (10 marks) In this question you must state if you use any...
3. (5 points each) Evaluate the following limits or state that they do not exist ("DNE"). Use or -- if either is appropriate. Numbers alone without justification (either algebra and/or quoting theorems where applicable) will receive no credit. If you use L'Hôpital's Rule, clearly indicate when you do so. +3 (a) lim (b) lim 1.-1 cot(0) (c) lim
MTH 251 Basic Limits Name: 1. Create a table of values and use it to "guess" the limit of the following expression: lim Vx +16-4 lim 2. Sketch the following piecewise function and evaluate the limits, if they exist: if-ISX<11 x2 if x21 f(x) = x b) lim f(x) c) lim f(x) a) lim f(x)- x->-I lim / (x)- e) lim/(x)- d) x→1 MTH 251 Basic Limits Name: 1. Create a table of values and use it to "guess" the...
Indeterminate limits are often difficult. Sometimes simplifying the expression allows us to evaluate the limit, but many times there isn't a good way of simplifying. L'Hospital's rule is used to more easily evaluate these indeterminate limits. While this rule doesn't always work or apply, it generally makes a limit easier to evaluate when it does apply. 1. List as many types of indeterminate limits as you can. 2. State l'Hospital's rule in your own words. (There are actually several versions...
S definition of limit or the Sequential Criterion for limits, to establish 2. (a) Use either the e - the following limits 1 lim i. lim n+2 = 4 ii ==1 2x +3 1- x n -1 T2 3x x2 - x + 1 1 ii. lim n 1 iv. lim n6 = 2 - 1 2 +3 S definition of limit or the Sequential Criterion for limits, to establish 2. (a) Use either the e - the following limits...
Evaluate the following limits. If you use L'Hopital's Rule, indicate on your paper that you have done so. If a limit is oo or - 0, then write oo or -oo. You may write DNE for does not exist. x² – 1 a.) lim Preview 7+1 In 4.q7 = - b.) lim 1+ I-4 2 – 3. - 4 Preview et -1 c.) lim 1+0 - sin(4x) Preview d.) limsin 4x = Preview Preview
3. (5 pts. each) Evaluate the following limits if they exist. If the limit does not exist, then use the Two-Path Test to show that it does not exist. 5x²y (a) lim (x,y)=(0,0) **+3y2 (b) lim (x,y)-(1,-1) 1+xyz
f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If the limit does not exist, explain why it does not exist Yon musi elearly staie if you ity, lopital's rle or the sandwch theorem in your working. You do not need to justify using limit laws. (i) lim f(x, y) (ii) im f(r, y (iv) zlin2-1.0 arctan ^Ca.v)l f(x, y) = y/(sqrt(z? + y2) + x) Evaluate the limits below, if they exist. If...
(4) Evaluate each of the following limits or show that the limit does not exist: (a lim 2014 – 2y4 (3,4) (0,0) 22 - y2 lim 1 + 2y (x,y) (0,0) = -2y (b)