MATH 100 Lecture Notes - Lecture 12: Antiderivative, Maxima And Minima

I1 points scalcET8 5.3.013 Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the func h(x)6 In(C) dt h(x) Need Help? Watch It Talk to a Tutor 5. Ό-11 points scalcET8 5.3019. Evaluate the integral. 14 (x2 + 2x -4) dx Watch Talk to a Tuter Talk to a Tutor Need Help? Read It

The height (in meters)of a projectile shot answers to two decimal places.) (Round your (a) Find the v(2) 4) b) When does the projectile reach its maximum height? ) When does it hit the ground? With what velocity does it hit the ground? 2/1/21 O Type here to search

SCalcET8 2.5.020 Explain why the function is discontinuous at the given number a. (Select all that apply.) if x 3 lim f(x) and lim f(x) are finite, but are not equal. a f(3) is undefined. x-+3+ lim f(x) does not exist. x-3 f(3) is defined and lim fx) is finite, but they are not equal. none of the above 0

0 ers SCalcET8 25045 MI For what value of the constant c is the function f continuous on (-00, 00)? ifXC5 f(x)-(cr2 + 6x Enhanced Feedback Please try again. Choose c so that the function is continuous at the point where once piece of the function end Need Help? |LRead It 」! L-Watch It..il L.Ma Talk to a

MATH 100 / MATH 109 UUsing Derivatives Using Derivatives... 1. ... to evaluate limits: (a) Explain why the limit lim +e* 100 et -e- is in a suitable form for applying l'Hospital's rule. (b) Attempt to evaluate lim ette will need to use l'Hospital's rule more than once to see the problem). 10 et -e- by applying l'Hospital's rule. What went wrong? (You (c) Without using l'Hospital's rule, show that lim +00 et -e-2 2. ... to optimize things: Of all the lines tangent to y = 12, find the equation of the one with the largest slope. 3. ... to approximate things: e* +e-* (a) Approximate ln(1.01) by using an appropriate linearization, and by using one iteration of Newton's method on an appropriate function. (b) Explain why we cannot use Newton's method to find a root of f(x) = 13 – 23 + 2 with initial guess 10 = 1. Illustrate your explanation with a sketch. Note: To see the problem you will need to do more than one iteration of Newton's method. 4. ... to prove things: (a) Prove that 25 + +1 has exactly one zero on [-2, 2). (b) Suppose that a runner completes a 3 mile race in 16 minutes. Assume that her initial speed is 0 and her speed at the end of the race is also 0. Prove that she was running at exactly 11 miles per hour at least two times during the race.

t of er = 4-2.2 Correct to six decimal places (6) (12 pts ] (a) Find a function f such that f, (z) = 13 and the line at +yO is tangent to the graph of f (b) F ind a general antiderivative of f(x) = 51:1/, s(x) + -3 sect + 2 co (7) [10 pts] Find the limit (a) lim VV rl 2-2 ) sin(t) (b) lim 3 (8) [10 pts] dy log (t2) dt. Find y(r) (a) y / /9_y2dt. Find y'(0) definition of the integral in terms of the limit of a Riemann sun to (b) x2- tan r 2t2 (9) [8 pts) Use the 4 evaluate 10) [10 pts] Evaluate the integrals (z-2)? 3