please help me with these 4 questions.

- 2 (2) Let h(z) = IIl Using the methods of this lesson, guess the slope of the tangent line to Z the graph of h at x = 1. What is the equation of that tangent line? (3) A car is driving along the z-axis. Its position at time is s(t) = t*. Using the methods of this lesson, determine the velocity of the car at time t = 3. (4) A weight on a spring is bobbing up and down. Its height above the ground at time is h(t) = 5+ cos2t. Determine the velocity of the weight at time t = 7. Be sure your calculator is in radian mode. (Degrees are seldom used in calculus.) (5) (Bonus question): A particle is moving back and forth on the z-axis. Its position at time t is s(t) = sint + cost. Construct a suitable table of values, and guess the velocity of the particle at time = 7. \fProblem 2: Tangent Line of h (x) = x+2 at x = 1 Interval Quotient h(x)-h(1) mpQ (Slope) [0.9, 1] 1.55-1.5 -0.5 -0.5 0.9-1 [0.99, 1] 1.505-1.5 0.99-1 =-0.5 -0.5 [0.999, 1] 1.5005-1.5 0.999-1 = -0.5 -0.5 [1, 1.1] 1.454545-1.5 1.1-1 = -0.454545 -0.4545.. [1, 1.01] 1.4950495-1.5 = -0.49505 -0.49505. 1.01-1 [1, 1.001] 1.4995005-1.5 1.001-1 = -0.4995 -0.4995. Final Answer for Problem 2: The slope of the tangent line at x = 1 is approximately -0.5.Problem 3: Velocity of a Car at t = 3 for s(t) = t2 Interval Quotient ()-s(3) t-3 Velocity [2.9, 3] 8.41-9_ 5.9 5.9 2.9-3 [2.99, 3] 8.9401-9 2.99-3 5.99 5.99 [2.999, 3] 8.994001-9 _ 5.999 5.999 2.999-3 [3, 3.1] 9.61-9 3.1-3 = 6.1 6.1 [3, 3.01] 9.0601-9 = 6.01 6.01 3.01-3 [3, 3.001] 9.006001-9 3.001-3 = 6.001 6.001 Final Answer for Problem 3: The velocity of the car at t = 3 is approximately 6 m/s.Problem 4: Velocity of a Weight at = 7 for h(t) = 5 + cos(2t) O Interval Quotient ; z( ) Velocity 4 ~ 1.7439 SRR ~ 1.9958 SRR T ~ 1.9999 ~ 1.9999 1.7439 ~ 1.7439 1.9958 ~ 1.9958 ~ 1.9999 ~ 1.9999 Final Answer for Problem 4: The velocity of the weight at = % is approximately 2 m/s