1. [-/1 Points] DETAILS SCALCET8 2.6.AE.012. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER EXAMPLE 11 Sketch the graph of y = (x - 3)*(x + 1)3(x - 1) by finding its intercepts and its limits as x -* * and x -+ ->. SOLUTION The y-intercept is 10) = (-3)*() (-1) = ]and the x-intercepts are found by setting y = 0: x = 3, 1, . Notice that since (x - 3)4 is positive, the function doesn't change sign at 3; thus the graph doesn't cross the x-axis at 3. The graph crosses the axis at -1 and When x is large positive, all three factors are positive, so Video Example Im (x - 3) (x + 1)3(x - 1) = *. When x is large negative, the first factor is large positive and the second and third factors are both large negative so X - -3 (x - 3)" (x + 1)3(x - 1) = 2. Combining this information, we give a rough sketch of the graph in the figure. Need Help? Bulk 2. [-/1 Points] DETAILS SCALCET8 2.6.AE.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Video Example EXAMPLE 6 Evaluate lim 2/x. SOLUTION If we let t = 2/x, we know that t - -* as x -0-. Therefore, by lim * = 0, lim 2/x = lim et = (See this exercise.) Need Help? Read 3. [-/1 Points] DETAILS SCALCET8 2.6.003. MY NOTES ASK YOUR TEACHER For the function / whose graph is given, state the following. (a) lim f(x) x - (b) lim f(x) (c) lim (d) lim, Kx) (e) the equations of the asymptotes (Enter your answers as a comma-separated list of equations.) vertical horizontal Need Help? .4. [-/1 Points] DETAILS SCALCETS 2.6.012. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Consider the function below (x) = (1- (a) Use a graph to estimate the value of the limit of lim f(x) correct to two decimal places. (b) Use a table of values of (x) to estimate the limit to four decimal places. Need Help? Reed 5. [-/1 Points] DETAILS SCALCETS 2.6.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the limit using the appropriate properties of limits. (If an answer does not exist, enter DNE.) lim 4x4 - 9 -+x 3x 2 + x - 3 Need Help? Hard max 6. [-/1 Points] DETAILS SCALCETS 2.6.015. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the limit, if it exists. (If an answer does not exist, enter DNE.) HIM 2x + 3 Need Help? Read me 7. [-/1 Points] DETAILS SCALCETS 2.6.025. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim V x + 6x2 -x 8x - 1 Need Help? Ased max 3. [-/1 Points] DETAILS SCALCETS 2.6.030.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim Vx2+ 3 Need Help? Reed 's 3. [-/1 Points] DETAILS SCALCETS 2.6.033. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the limit, if it exists. (If an answer does not exist, enter DNE.) -42 (x2 + 2x9) Need Help? Rard * max 10. [-/1 Points] DETAILS SCALCETS 2.6.037. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the limit. lim 8 - ex X -* 8+ 92* Need Help? Remix11. [-/1 Points] DETAILS SCALCETS 2.6.045. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (a) Estimate the value of lim (Vx2 + x + 6 + *) by graphing the function ((x) = \\ x2 + x + 6 + x. -30 -20 30 -60 -30 -20 (b) use a table of values of f(x) to guess the value of the limit. (Round your answer to one decimal place.) (c) Prove that your guess is correct by evaluating lim f(x)- Need Help? Read me35 12. [-/1 Points] DETAILS SCALCETS 2.6.049. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the horizontal and vertical asymptotes of the curve. y = &* + x - 9 x2 +x - 42 X= (smaller x-value) x= (larger x-value) Need Help? Read 13. [-/1 Points] DETAILS SCALCETS 2.6.050. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the horizontal and vertical asymptotes of the curve. y = 1+x (smallest x-value) * = (largest x-value) y= 14. [-/1 Points] DETAILS SCALCET8 2.6.057. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find a formula for a function / that satisfies the following conditions. lim (x) = 0, lim (x) = -x, (6) = 0 xorg ((x) = =, lim f(x) = -3 ((x ) = Need Help? And Women15. [-/1 Points] DETAILS SCALCET8 2.6.055. MY NOTES ASK YOUR TEACHER Let P and Q be polynomials with positive coefficients. Consider the limit below. lim P(x) *-+x Q(x) (a) Find the limit if the degree of P is less than the degree of Q. (b) Find the limit if the degree of P is greater than the degree of Q. ead Help? Rand mix 16. [-/1 Points] DETAILS SCALCET8 2.6.069. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER In a later chapter we will be able to show, under certain assumptions, that the velocity v(t) of a falling raindrop at time t is v(t) = vy(1 - e-9t/vT) where g is the acceleration due to gravity and vy is the terminal velocity of the raindrop. (a) Find lim v(t). (b) Graph v(t) if vy = 8 m/s and g = 9.8 m/s2. (A graphing calculator is recommended.) (c) How long does it take for the velocity of the rain drop to reach 99% of its terminal ve from part (b). Round your answer to two decimal places.) Need Help? Reed moment 17. [-/1 Points] DETAILS SCALCETS 2.6.076. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER How large do we have to take x so that 1/v x 0 there is a number & > 0 such that if 0 0 there is a corresponding number / such that if x > N then [(x) - L| 0 there is a number & > 0 such that if 0 0 there is a corresponding number / such that if x > N then [x) - L|