Can someone check and finish

CALCULUS WEEKLY REVIEW # 10 2. A streetlight is 15 feet tall. A boy who is 6 1. For what value of k does the limit exist? feet tall is walking away from the light at a rate of 5 feet/s. Determine the rate at which his shadow is lengthening at the lim * 2 + 3x + k K = - JO moment he is 20 feet from the light. 1 - 2 x - 2 152+62 = c 2 5 ( X - 2 ) ( * + 5 ) = * + 3x - 10 if = 2 dc ,d+ 2 (5) = 2dc SHADOW &C = 5 f+15 2 ft/ sec 3. Set up the limit definition for finding 4. Find the values of a and b so the the derivative of y = sin x. function will have a relative extreme at f ( xth ) - f( x ) sin( xth ) - sin(x ) (3, 1). - x3 + ax 2 + b h h y ' = * + zax = 0+ a = - x 2 x 5. Find the equation of the tangent line to 6. If 8(x) = x'+x2+-, find the value of the curve y = x2 - 3x at the place where the 8"(2). parabola crosses the y-axis. X = 0 y = 0 g( x ) = x 3 + x 2 + x - 1 1 = 2 x - 3 slope = - 3 g'l x ) = 3x 2 + 2 x - x- 2 y - 0 = - 3( x - 0 ) 9" ( * ) = 6*+ 2 + 2 x- 3 y = - 3x g" ( 2 1 = 6 (2) + 2 + 2/2)-3 2 51 / 4 7. If h(x)=2x-3), what is the value of 8. What is the value of c guaranteed to the derivative at x = -2? exist by the Mean Value Theorem if h' ( 1 ) = 2 . 2 x - 3 = - 2 m(x) = x4 - 3x over the interval [1, 3]. 12 x- 3 ) n'1 - 2 ) = 2 . 21- 2 ) - 3 |21-2)- 31 9. This is the graph of the velocity of a given particle moving along the x-axis in meters/ second. At what time(s) does the particle 10. Continuing #9, how far did the particle reverse direction? move during the 10 seconds shown on the graph? [2, 7] -6 m / 4 5 6/7 8 9 1 interval