# SUNY Broome MAT 181 - Sample Questions MAT 181 (2 pages)

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## Sample Questions MAT 181

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- Pages:
- 2
- School:
- SUNY Broome Community College
- Course:
- Mat 181 - Calculus I

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Sample of Material from MAT181 at Broome Community College This material is for sample purposes only and is not to be considered as an official listing of topics x3 1 accurate to 8 decimal places x 1 sin x 1 1 Set up a table of values to evaluate lim 2 Evaluate the following limits algebraically or with L Hopital s Rule 1 e 2x x 0 sin x b lim a lim x 7x 4 7 4x 2 3 Using your answer from 2 explain whether f x 7x 4 7 4x 2 has a horizontal asymptote If so state the equation 4 Use the limit definition of the derivative to help find the equation of the tangent line to 1 f x x when x 10 x 5 Using the Power Product and Quotient rules find the derivative for the following functions Factor and or reduce where possible a f x sin2 x b y 2 c h x e x tan x x ln x d p x ln secx 6 Graph a single function that has all of the following properties a f 0 1 f 5 0 b c f 1 0 and f 4 0 d lim x 2 f x and lim x 2 f x lim lim f x f x x x e f x 0 on 1 and 1 2 and 2 4 f x 0 on 4 f f x 0 on 1 2 f x 0 on 1 and 2 7 Find the equation of the tangent line to sinx y2 5y x 10 at the point 0 2 8 Use derivatives to find the critical values for f x 1 4 x 8x 2 5 then set up a table to find 4 the extreme values on 2 5 9 A fishing boat lays a circular net in the water If the netting is pulled in at 20 ft minute how fast is the radius of the circle decreasing when the diameter of the net is 100 feet Set up an equation and show a Calculus answer Net 10 Evaluate the following antiderivatives Show the Change of Variables in each case a x 2 sec 2 x 3 4 dx b cos x 2 sin x dx 11 Find the area of the region bounded by f x 8 x2 and y 2x Evaluate the integral using the Fundamental Theorem of Calculus 12 Find the volume of the solid formed when the region trapped between y x2 y 0 and x 3 is rotated around the line x 3 State the method you are using 13 A car traveling 60 feet per second accelerates at 20 feet per second2 a Use calculus to derive a position function Note you must derive the function not copy a finished

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