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1. [or Poles] DETAILS PREVIOUS ANSWERS OSCALCI 3.1.803. Line the equation gin John And that tops of the BEE on the value s; and fy for the function ; = fr) Or+ 4 2. [-47 Paint] DETAILS 65CALC1 3.1.805.TUT.SA. Y - H Like the equation gu bills to find the dogs of the secant line between the valuem s, and a, far them 12 Ascall that the differsoon quotient forrule, Q . 4912 clean the alope of the ascent Ins between the palms [a, Mall and [y, hajj on the graph of y = As]. To use the gives difference quotient forwards, we nearits It by replacing the s and a withs, ands,. respectively. 8 - 1 3. [ /1 Points] DETAILS OSCALCI 2. 1.091. r- Line the scumtion gimlilists And that tops of the cast Ina between the valen , and my for the function ; = had12. [-ISPoints] I DETAILS I 05CALC13.1.033. Consider the function y = x). x) = men-2", P(0, 10) (a) Find the slope of the secant line PQ for each point Q(x, x\" with the x value given in the table. (Round your answers to four decimal places.) x Slope mm *0-1 |:| -0-001 |:| 70.0001 |:| o.ooo(11 |:| o.oooom |:| (b) Use the answers from part (a) to estimate the value of the slope of the tangent line at F. :i (c) Use the answer from part (b) to nd the equation of the tangent line to fat point P. (Letx be the independent variable and y be the dependent variable.) 13. [-16 Points] DETAILS 05CALC1 3.1.037. For the following position function y = 5(I'), an object is moving along a straight line, where tis in seconds and s is in meters. 50) = 2:3 + 3 (a) Find the simplified expression for the average velocityr from f = 2 to t = 2 + h. (b) Find the average velocity between t = 2 and t = 2 + h, where h = 0.1, h = 0.01, h = 0.001, and h = 0.0001. (Round your answers to three decimal places.) h averagewelocity (c) Use the answers from part (b) to estimate the instantaneous velocity at f : 2. :l 4. [-/1 Points] DETAILS OSCALC1 3.1.010. Use the equation Q = _ to find the slope of the secant line between the values x] and X2 for the function y = f(x). x - a f( x ) = 8x2/3 + 4x1/5; x1 = 1, X2 = 8 5. [1/9 Points] DETAILS PREVIOUS ANSWERS OSCALC1 3.1.011-020.WA.TUT.SA. This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find the equation of the line tangent to the given curve at the given point. y = Vx; (16, 4) Step 1 of 5 Recall the limit definition of the derivative of a function y = f(x) at a number a. This is the slope slope of the tangent line to y = f(x) at x = a. f'(a) = lim f(x) - f(a) X - Step 2 of 5 To write the equation of the line tangent to the curve y = v x at the point (x, y) = (16, 4), we will need the slope of that tangent line and a point on the tangent line. Use the limit definition of derivative to find the slope of the tangent line, Means to y = v x at x = 16. mtan = f'(16) = lim f(x) - f(16) - 16 X - 16 lim x - 16 x - 16 Submit Skip (you cannot come back)Consider the function and the value of a. x)=+5,a=1 to nd the slope of the tangent line mtan = f'(a). (b) Find the equation of the tangent line to fat x = a. (Let x be the independent variable and y be the dependent variable.) S, ?. [112 Points] DEFAILS PREVIOUS ANSWERS OSCALC1 3.1.016. Consider the function and the value of a. x): v'x+ 15,a=1 (3} Use mtan: \"[11 M h'D h to nd the slope of the tangent line mtan = f'(a). tan _1 m'8 J (b) Find the equation of the tangent line to fat x = a. (Let x be the independent variable and y be the dependent variable.) Ex 3. [-!2 Points] DETAILS OSCALC1 3.1.020. Consider the function and the value of a. ' We) nd the slope of the tangent line mtan = f'(a). (b) Find the equation of the tangent line to Fat x = a. (Let x be the independent variable and y be the dependent variable.) S 9. [-/1 Points] DETAILS OSCALC1 3.1.021. For the function y = f(x), find f'(a) using mean = lim- F(x) - f(a ) x - a f(x) = 5x + 4, a = -1 f'(a ) = 10. [-/1 Points] DETAILS OSCALC1 3.1.028. For the function y = f(x), find f'(a) using mean = lim f(x) - f(a ) e-X x - a = (x) 1 a = -5 x - 1 f'( a ) = 11. [-/1 Points] DETAILS OSCALC1 3.1.030. For the function y = f(x), find f'(a) using mean = lim f (x ) - f(2 ) x - a A( x ) = a = 9 f' ( a ) = +
