Is increasing when x 1 14 t f the derivative of 1 1 x

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is increasing whenx >1.(14)TF
The derivative of 1/(1 +x2) is equal to arctan(x).(15)
Problem 2. (Dierential calculus)(10 points)(1) (3 points) Compute the limit limx!01ex-1-1x.(2) (3 points) Use linear approximation to estimate ln(0.998).(3) (4 points) Find equations of both the tangent lines to the ellipsex2+9y2= 81 that pass throughthe point (27,3).Problem 3. (Indefinite integrals)(33 = 9 points). Compute the following indefinite integrals.UseCto stand for the constant of integration.1
Math V1101: Calculus I (Chao Li)Final Exam (Sample)(1)Z7px8dx.(2)Zsec2xtan4x dx.(3)Zx5x6-3dx.Problem 4. (Definite integrals)(34 = 12 points).(1)Z10e-3xdx.(2)Z103p1 + 7x dx.(3)Z6p0x5cosx6dx.(4)Z0-3(1 +p9-x2)dx.Problem 5. (Curve sketching)(5 points).Consider the functionf(x) =Zx1(t2-4t-5)dt.(1) Find the intervals on whichf(x) is increasing or decreasing.(2) Find the intervals on whichf(x) is concave up or concave down.(3) Use the above information to sketch the graph ofy=f(x).Problem 6. (Area)(4 points).The cat head is enclosed by the functionsf(x) =x20-1 andg(x) =x2-x6. Find its area.Problem 7. (Net change)(5 points).The cat in Problem 8 is running with the acceleration functiona(t) =t+ 5. Its initial velocityisv(0) = 4 m/s.(1) Find its velocity functionv(t) at any timet.(2) Find the distance traveled during the time interval 0t8.2

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