By James Stewart
Comprises key recommendations, abilities to grasp, a quick dialogue of the information of the part, and worked-out examples with tips to find the answer.
Read Online or Download Study Guide for Stewart's Single Variable Calculus: Concepts and Contexts, 4th PDF
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Extra resources for Study Guide for Stewart's Single Variable Calculus: Concepts and Contexts, 4th
Sample text
2. Graph the function y = x4 − 100x2 Try to choose a viewing area that captures all important details. 10. 3. Use graphs to find the solutions to the equation x2 = sin x correct to two decimal places. Graph y = x2 and y = sin x in the same graph and zoom in on the intersection points. 4. 11. 4. Graph the function y = x2 − 2cx for various values of c. What is this family of functions and how does the graph change as c varies? Confirm your guess by analyzing the graph using algebra. Try c = −2, c = −1, c = 0, c = 1, c = 2.
001. 4. Estimate the equation of the tangent line at the point (1, 2) in the graph below. 2 0 1 2 3 First notice that f (0) = 03 − 4(0) = 0. Form the slopes of the secant lines PQ which are given by f (x) − f (0) f (x) = x−0 x Sketch the tangent line on the graph. Sketch in a right triangle that has part of this tangent line as the hypotenuse. Estimate the slope by dividing the length of the vertical side of the triangle by the length of the horizontal side of the triangle. Use this as the slope in the equation of the tangent line in point-slope form.
Estimate the equation of the tangent line at the point (1, 2) in the graph below. 2 0 1 2 3 First notice that f (0) = 03 − 4(0) = 0. Form the slopes of the secant lines PQ which are given by f (x) − f (0) f (x) = x−0 x Sketch the tangent line on the graph. Sketch in a right triangle that has part of this tangent line as the hypotenuse. Estimate the slope by dividing the length of the vertical side of the triangle by the length of the horizontal side of the triangle. Use this as the slope in the equation of the tangent line in point-slope form.
