Finding an Equation of a Tangent Line In Exercises 59-62, (a) find an equation of the tangent line to the graph of the function at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a graphing utility to confirm your results.
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Chapter 3 Solutions
Calculus: Early Transcendental Functions
- Identify the graph of the trigonometric functionf(x) cscx (а) (b) (c) (d)arrow_forwardUse a graphing utility to graph each function in the interval [0, 2x). y = 9 cos?(x), y = 9e-x + 9x - 9 (a) Write an equation whose solutions are the points of intersection of the graphs. (b) Use the intersect feature of the graphing utility to find the points of intersection (to four decimal places). (Enter the point of intersection whose x-coordinate is within the interval [o, 27). If there is no solution, enter NO SSOLUTION.) (x, y) =arrow_forwardFill in the blank/s : sin(-t) = ______ , csc(-t) = ______ , tan(-t) = ______ , and cot(-t) = _____ , so the sine, cosecant, tangent, and cotangent are ______ functions.arrow_forward
- Question What is the cosine equation of the function shown?arrow_forward(a) Find the amplitude, period, and horizontal shift. (Assume the absolute value of the horizontal shift is less than the period.) amplitude period horizontal shift (b) Write an equation that represents the curve in the form y = a cos(k(x − b)).arrow_forward. Energy Usage A mathematics textbook author has determined that her monthly gas usage y approximately follows the sine curve y = 12.5 sin(t + 1.2)) + 14.7, where y is measured in thousands of cubic feet (MCF) and t is the month of the year ranging from 1 to 12. (a) Graph this function on a graphing calculator. (b) Find the approximate gas usage for the months of February and July. (c) Find dy/dt, when t = 7. Interpret your answer. (d) Estimate the total gas usage for the year.arrow_forward
- The force F (in pounds) on a person's back when he or she bends over at an angle from an upright position is modeled by 0.6W sin(+90°) F = sin(12⁰) where W represents the person's weight (in pounds). (a) Simplify the model. F (b) Use a graphing utility to graph the model, where W = 175 and 0° ≤ 0 ≤ 90°. At what angle (in degrees) is the force maximized? A = 。 At what angle (in degrees) is the force minimized? 0 =arrow_forwardWrite a function in degree mode and a function in radian mode to model the grap h(t) = (43) 04-) h(t) =arrow_forward
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