MAT 21B Lecture Notes - Lecture 10: Royal Institute Of Technology

A ball is kicked upwards and its height follows this equation, where f(x) is the height and x is the number of seconds after the kick: 1. f(x) =-16x,16x Find the speed (the instantaneous rate of change in height), using the derivative r(x) . Now find the speed at the following times 0 seconds after the kick: 0.5 seconds after the kick: f(o) (o.5) 2 Find the average rate of change between the indicated points: y-f(x) -3 x y=f(x)=4x x10, x=2 x=0, x:3 x-0, x-3

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

1. 0/6 points LarCalc11 13.1.010. [3864 VIA Evaluate the function at the given values of the independent variables. Simplify the results. fx, y) -4 -x2 - 4y2 (a) ro, 0) for (c) f2, 3) (e) x, o Cal 2. 0/2 points LarCalc11 13.1.019.MI. [386 Evaluate the function at the given values of the independent variables. Simplify the results. x, y)- 6x y2 (a) fix + ax, y)-f(x, y) Ay

3. 1 points LarCalc11 13.2 Find the indicated limit by using the limits limfx, y) 2 and im g(x, y)--4 lim 4. O/1 points LarCalci1 13 2 Find the indicated limit by using the limits lim x, y) 3 and lim (x, y) g(x, y)--5 (a, b) lim x, Y) (x, y) (a, b) g(x, y) 5. y1 points LarCalc11 13.3 Explain whether or not the Quotient Rule should be used to find the partial derivative. Do not differentiate. ay x2 51 O Yes, the function is a quotient. O No, y only occurs in the numerator. 6. 0/2 points LarCalc11 13.3 Find both first partial derivatives oz 7. 0/2 points LarCalc11 13.3 Find both first partial derivatives. hx, y) ex+y) h(x, y)

8. /2 points LarCalc11 13.3.031 Find both first partial derivatives. az dx az ay 9. /1 points LarCalc11 13.4.003. Find the total differential. z 3xSy10 dz 10. 0/2 points LarCalc11 13.5.012 Consider the following. (a) Find dw/dt using the appropriate Chain Rule. dw dt (b) Find dw/dt by converting w to a function of t before differentiating. dw dt 11. 0/1 points LarCalc11 13.6.008. Find the directional derivative of the function at P in the direction of v. rx, y) = x3-y3, Rio, 9), v-V2 (1+j)

12. 0/2 points LarCalc11 13.7.017 (a) Find an equation of the tangent plane to the surface at the given point. x+y+z=9, (2, 5, 2) (b) Find a set of symmetric equations for the normal line to the surface at the given point. ox -2y -5-z-2 13. /3 points LarCalc11 13.8.025 Use a computer algebra system to graph the surface and locate any relative extrema and saddle points. (If an an not exist, enter DNE.) -8x x2 y21 relative minimum (x, y, z) - relative maximum (x, y, z) saddle point 14. 0/1 points LarCalci1 13.10.027 Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated point. Surface Point Plane: x yz 1 (7,1,1)