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Determine the following limits. If the value is infinite, specify inf or -inf with enough justification for which. If an
answer does not exist, explain why
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- 4. Find Lim?→0^+ (1/(e^x - 1) - 1/x)a. Graph h(x) = x2 cos (1/x3) to estimate limx-->0 h(x), zooming in on the origin as necessary. b. Confirm your estimate in part (a) with a proof.Given lim (4x-3) as x approaches 1. Use the definition of a limt to find a number delta such that the absolute value of x-a is less than delta when the absolute value of f(x)-L is less than 0.08
- (3) Using the appropriate approach covered in Unit 6 of this Course along with knowledgegained in Unit 1 and 2, show that: (a) Limx→0 (1/x-1 +1/x+1)/x = -2 (b) Limh→0 (h/√5h + 4 − 2) = 4/5(c) Limt→1(t3- 1/t-1) = 3determine the limit limh→0[(x+h)2-x2]/h by treating x as a constant. determine the limx→0cos(2x)/x determine the limx→0 sin(2x2)/xtan(4x) Thanks in advance.Let ƒ(x) = (x2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01, -3.001, and so on as far as your calculator can go. Then estimate limx--> -3 ƒ(x). What estimate do you arrive at if you evaluate ƒ at x = -2.9, -2.99, -2.999,...... instead? b. Support your conclusions in part (a) by graphing ƒ near c = -3 and using Zoom and Trace to estimate y-values on the graph as x -->-3.
- (b) Use your answers from above to determine lim t→0- (5t -1)/t. In your own work, you may want to add more values to the table from above. (d) Use your answers from above to determine lim t→0+ (5t -1)/t In your own work, you may want to add more values to the table from above. (e) Use your answers from parts (b) and (d) to find lim t→0 (5t -1)/t1. Is it possible that f(2) = 5 but limx→2f(x) = 7? If so, what kind of function can satisfy this?Evalute the limit of: lim x->0 (x csc 6x)/(cos 14x) The answer must be in simplified form or a fraction
- Let ƒ(x) = (x^2 - 9)/(x + 3). a. Make a table of the values of ƒ at the points x = -3.1, -3.01, -3.001, and so on as far as your calculator can go. Then estimate limxS -3 ƒ(x). What estimate do you arrive at if you evaluate ƒ at x = -2.9, -2.99, -2.999,c instead? b. Support your conclusions in part (a) by graphing ƒ near c = -3 and using Zoom and Trace to estimate y-values on the graph as xS -3. c. Find limxS -3 ƒ(x) algebraically.8x+4-4cos’x+tanx 4sin2x Q1) Find lim x-0 V10 Q2) Find lim = x~0Find limx->0+(x/ln(x)).Please explain all the steps and rules used to figure out the answer as I'm studying it rigorously. Thank you so much!