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pleas answer all the questions correctly, make sure to answer all parts of each question .

B webassign.net 3. [-125 Points] SCALCET8 2.1.003. 0/5 Submissions Used The point P(4, 3) lies on the curve y = 3/(3 x). (a) If Q is the point (x, 3/(3 - X)), use your calculator to nd the slope mm of the secant line PQ (correct to six decimal places) for the following values of x. (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(4, 3). m = (c) Using the s ope from part (b), find an equation of the tangent line to the curve at P(4, 3). (i) me _ 1 (ii) 3.99 l l m\": l ' (iii) 3.999 l m = Po 1 (iv) 3.9999 1 mm: m l (v) 41 l "'Po= l l (Vi) 4.01 l "7\": l l (vii) 4.001 l mPo= i l l (viii) 4.0001 l \"7P0: l l l l l l l l l l l l l l l ASK YOUR TEACHER 3. [-/12.5 Points] DETAILS SCALCET8 2.2.AE.007. 0/5 Submissions Used MY NOTES ASK YOUR TEACHER EXAMPLE 7 The graph of a function g is shown in the figure. Use it to state the values (if they exist) of the following (a) lim g(x ) ( b ) lim g ( x ) (c) lim g(x) x - 2- x - 2+ x - 2 - 3 (d) lim g(x) x - 5 - (e) lim g(x) x - 5+ (f) lim_g(x). 2 SOLUTION From the graph we see that the values of g(x) approach 4 as x approaches 2 from the left, but the 1 approach 0 as x approaches 2 from the right. Therefore (a) lim g(x) = and (b) lim g(x) = -2 2 6 x - 2- x - 2+ Video Example () (c) Since the left and right limits are different, we conclude that the limit as x approaches 2 of g(x) does not exist. The graph also shows that (d) lim g(x) = and (e) lim g(x) = x - 5 + (f) This time, the left and right limits are the same and so, by this theorem, we have lim_g(x) = x- 5- Despite this fact, notice that g(5) # 1.+ 88 Prove the statement using the &, o definition of a limit. n 1 + - x = 2 Given & > 0, we need 8 (---Select--- @ such that if 0 (1+ 2x) - 2