Questions and Answers of Applied Calculus

Find the slopes and y-intercepts of the following lines.y = 6
Find the first derivatives.g(y) = y2 - 2y + 4
What can you say about the slopes of parallel lines? Perpendicular lines?
Estimate the slope of each of the following curves at the designated point P. P
Is the function, whose graph is drawn in Fig. 7, continuous at the following values of x?x = .001 + -5 -4 -3 -2 -1 Figure 7 y 1 2 3 + 4 5 X
Suppose that f(x) = -6/x.(a) What is the average rate of change of f (x) over each of the intervals 1 to 2, 1 to 1.5, and 1 to 1.2?(b) What is the (instantaneous) rate of change of f (x) when x = 1?
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions.f(x) = x7
Find the slopes and y-intercepts of the following lines.x = 2y - 3
Find the equation and sketch the graph of the following lines.Through (2, 0), with slope 5.
For each of the following functions g(x), determine whetherexists. If so, give the limit. lim g(x) x-3
Is the function, whose graph is drawn in Fig. 7, continuous at the following values of x?x = 3 + -5 -4 -3 -2 -1 Figure 7 y 1 2 3 + 4 5 X
Estimate the slope of each of the following curves at the designated point P. P
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions. f(x) = 3.x 4 2
Find the first derivatives.v(t) = 4t2 + 11√t + 1
Estimate the slope of each of the following curves at the designated point P. P
Is the function, whose graph is drawn in Fig. 7, continuous at the following values of x?x = 0 + -5 -4 -3 -2 -1 Figure 7 y 1 2 3 + 4 5 X
Suppose that f(x) = 4x2.(a) What is the average rate of change of f(x) over each of the intervals 1 to 2, 1 to 1.5, and 1 to 1.1?(b) What is the (instantaneous) rate of change of f (x) when x = 1?
For each of the following functions g(x), determine whetherexists. If so, give the limit. lim g(x) x-3
Differentiate.y = 33√x
Find the equation and sketch the graph of the following lines.With slope 3/4, y-intercept (0, -1).
Find the first derivatives.f(P) = P3 + 3P2 - 7P + 2
Differentiate.y = 6x3
If f(x) = x2 + 3x, calculate the average rate of change of f(x) over the following intervals(a) 1 ≤ x ≤ 2,(b) 1 ≤ x ≤ 1.5,(c) 1 ≤ x ≤ 1.1.
Find the first derivatives.f(t) = (t2 + 1)5
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions.f(x) = 3x + 7
Find the equation and sketch the graph of the following lines.With slope -2, y-intercept (0, 3).
Differentiate.y = 3x4
Use formulas (1) and (2) and the power rule to find the derivatives of the following functions.f(x) = -2x
Estimate the slope of each of the following curves at the designated point P. P I
If f(x) = 3x2 + 2, calculate the average rate of change of f(x) over the following intervals(a) 0 ≤ x ≤ .5,(b) 0 ≤ x ≤ .1,(c) 0 ≤ x ≤ .0.01.
Is the function, whose graph is drawn in Fig. 7, continuous at the following values of x?x = -3 + -5 -4 -3 -2 -1 Figure 7 y 1 2 3 + 4 5 X
For each of the following functions g(x), determine whetherexists. If so, give the limit. lim g(x) x-3

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