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MATH151 Fall 2022 Common Exam I Version A FIRST NAME print LAST NAME print INSTRUCTOR SECTION NUMBER DIRECTIONS No calculators cell phones smart watches headphones or other electronic devices may be used and must be put away TURN OFF cell phones and put them away If a cell phone is seen during the exam your exam will be collected and you will receive a zero In Part I mark the correct choice on your ScanTron using a No 2 pencil The scantrons will not be returned therefore for your own records also record your choices on your exam In Part II present your solutions in the space provided Show all your work neatly and concisely and clearly indicate your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it Be sure to fill in your name UIN section number and version letter of the exam on the ScanTron form THE AGGIE HONOR CODE An Aggie does not lie cheat or steal or tolerate those who do Signature 1 Part I Multiple Choice 3 points each 1 Find a vector of length 3 in the same direction as the vector from the point 2 3 to 1 1 a 9 12 12 9 5 5 b 512 5 c d e 9 5 3 6 5 5 5 17 12 3 2 Find a vector equation of the line that passes through 6 4 and is perpendicular to the line with parametric equations x 7 2t y 1 3t a r t 4 3t 6 2t b r t 6 t 4 7t c r t 6 2t 4 3t d r t 4 2t 6 3t e r t 6 3t 4 2t 3 Find lim a b c 0 d ln 5 2 e 3 ln 5x2 1 ln x3 x 4 x 2 4 Find the cosine of the angle between the vectors 3 5 and 2 1 11 34 5 a b 11 2114 51 c d 34 5 30 e 34 5 5 Find the scalar projection of b 3i 2j onto a 2i 5j 4 2 b 344 c 294 e 29 4 d 13 6 Find lim 23 a x 2 b 92 c 92 d 3 e 2x 3 9x 2x 5 0 2 3 x2 x2 x a b c d 7 Which of the following is equal to tan arccos x 2 4 x 4 4 x2 2 x 4 x2 2 e 4 x2 3x 6 8 Find lim a b 0 c 3 d 12 x 2 e 9 The position in meters of a particle after t seconds is given by f t t 1 2 1 Find the average velocity of the particle from t 1 to t 3 a 8 m s b 4 m s c 6 m s26 m s d 3 e 9 m s x 2 4 x 5 f x 5 f x 1 f x Use the following graph of f to answer questions 10 and 11 10 Given the graph of f above which of the following is false a lim b lim c f is continuous from the left at x 3 d limx 5 e f is continuous at x 1 11 Given the graph of f above for which value of x is f x differentiable a x 3 b x 3 c x 1 d x 1 e x 2 x 3 5 ax2 2x if x 2 3x a if x 2 continuous everywhere 12 A crate is hauled 10 meters up a ramp under a constant force of 7 Newtons applied at an angle of 30 to the ramp Find the work done a 35 2 J b 35 J c 70 J d 35 3 J e None of these 13 Find the value of a that makes f x a 210 b 32 c 3 d 4 e There is no such a value 14 According to the Intermediate Value Theorem which of the following intervals contains a solution to the equation x3 4x 5 0 a 2 1 b 0 1 c 1 0 d 2 3 e 1 2 6 4x x2 5x 3x 15 Find lim x 4 a 35 b 3 c 1 d e x 5e 2x 3e4x 2e 2x e4x 16 Find lim a 3 b 0 c 5 d 2 e 17 Which of the following correctly describes the curve given by r t 1 sin t 2 cos t as t increases a Clockwise around a circle with center 1 2 b Counterclockwise around a circle with center 1 2 c Clockwise around a circle with center 1 2 d Counterclockwise around a circle with center 1 2 e None of these 7 x2 x3 x 4 2 x x 3 18 Find the horizontal and vertical asymptotes of f x a y 1 x 2 x 3 b y 1 x 3 c y 1 x 3 d y 1 x 2 e y 1 y 1 x 3 19 Find lim arctan x x 7 a 2 b 4 c 4 e 2 20 Given f x x3 4x 1 and f x 3x2 4 find the equation of the tangent line to f x at x 2 a y 8x 10 b y 8x 1 c y x 10 d y 8x 17 e y x 3 d 8 Part II Work Out Problems Directions Present your solutions in the space provided Show all your work neatly and concisely and box your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 21 10 points Two forces F1 and F2 act on an object The force F1 has a magnitude of 26 lbs and a direction of 45 counterclockwise from the positive x axis and F2 has a magnitude of 8 lbs and a direction of 150 counterclockwise from the positive x axis a Find the resultant force F b Find the resultant angle as measured counterclockwise from the positive x axis Leave your answer in terms of an inverse trigonometric expression 9 22 15 points Find the following limits Do not use L Hospital s Rule a limx 6 x 2 2 16 x2 6x x 2 b lim 5x 6 4 x 2 x 1 c lim x 1 x2 3x 2 10 2ex 3 if x 3 3x 1 if 3 x 1 x2 3if x 1 f x or explain why it does not exist f x or explain why it does not exist 23 6 points Consider the function f x a Find limx 3 b Find lim 24 9 points Use the definition of the derivative to find f x for f x 4 No points will be given x 1 for any shortcut formulas used x 2 11 Do not write in this table Question Points Awarded Points 1 20 60 10 21 22 15 6 23 24 9 100 Total …

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