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- Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?Experiment 1: 1D. State the slope of the tangent line by substituting x = 2 into the derivative f'(x). State the value f'(2). 1E. Does f'(2), the y-coordinate on the gray line at x = 2, have any relationship to the derivative value f'(2)? 1F. Does f'(2), the y-coordinate on the gray line at x = 2, have any relationship to f(2), the y-coordinate on the parabola at x = 2?Experiment 3: 3D. Does f'(0), the y-coordinate on the gray line at x = 0, have any relationship to the derivative value f'(0)? 3E. Does f'(0), the y-coordinate on the derivative line at x = 0, have any relationship to f(0), the y-coord. on the parabola at x = 0?
- Compute f'(x). f(x)= 8x^-3 , a=5 f'(x)=____________ Find an equation of the tangent line to the graph at x = a. (Enter your answer as an equation using the variables y and x.) _______________________A. Find the equation of the tangent line to the curve y=(x-1)^ 5 (x+4)^2 at the point (2,36). The equation of the tangent line to the curve at the given point is y=_________ B. Differentiate the function. y= [(2x^2+4x+3)(x-9)]^2Struggling with applied calc: Find an equation for the tangent line to the following curve, h(x) = 11x - 3 ln x at the point where x = e.
- Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If V is the volume of such a cube with side length x, calculate the derivative when x = 5 mm. V'(5) = mm3/mm What does V'(5) mean in this situation? V'(5) represents the rate at which the volume is increasing with respect to the side length as V reaches 15 mm3.V'(5) represents the volume as the side length reaches 5 mm. V'(5) represents the rate at which the volume is increasing as x reaches 15 mm.V'(5) represents the rate at which the side length is increasing with respect to the volume as x reaches 5 mm.V'(5) represents the rate at which the volume is increasing with respect to the side length as x reaches 5 mm.Compute the derivative function f′(a) algebraically for the given value of x.f(x) = −x − x2; a = 0 Find the equation of the tangent to the graph at the indicated point of a = 0 for using the function and information found from Hint: to find a linear equation, we need a slope and a point.Find y'' (the second derivative) of y = (1 + 1/x)^3. Please get the answer in the form of (6 / (x^3))(1 + 1/x)(1 + 2/x).