Math 151 final Exam Review 1 All of problem 1 refers to the line x 3y 5 a Find a vector v that is perpendicular to the line J Lewis b Verify that the point Q 2 1 is on the line Find the distance from the point P 3 2 to the line 2 Find the scalar component and the vector component of 7 4 in the direction of 2 3 What is the angle between these two vectors a At what values of x is f not continuous and why is f not continuous there b At what values of x is f not differentiable and why not At what values of x is f not differentiable What is seen in the graph at 4 these x values 5 For all of problem 2 a Find the equation of the tangent line to f x at 1 f 1 b Find the tangent line approximation linear approximation to f 1 1 Do not round 6 a Find the linear approximation to b Find the linear approximation linearization of for t near 0 3 xxxxxxxxxfx525326369 23312 34 xxxf11 2 xxxxf55 31t 1 7 For problem 3 a Verify that f is continuous It is understood that lines and quadratics are continuous b Find all values of x at which f is not differentiable Justify your answer either with a graph or some other means 8 For problem 4 a Find f x b For find g 1 9 Simplify each expression 10 A blimp is traveling at the constant height of 40 feet with constant speed 5 feet per second always in the same direction A boy on the ground watches the blimp move away from him What is the rate of change of the angle between the horizontal and a line from the boy to the blimp at the instant that the distance between them is 50 feet 11 A person rows a boat at 3 mph and walks at 4 miles per hour He is on an island that is 8 miles from shore He wants to reach a cabin that is 12 miles down shore At what point on shore should he tie his rowboat and walk to minimize his travel time 12 A curve is given parametrically by Find the points on the curve where the tangent line is horizontal and where it is vertical xxxxxxxxf3124313214 211 1 arcsin 2 23 xxxxf 1xfxg 3 sin arctan arcsin2tan 2 sec arcsin 53 sec arcsin tdxcxbatettytttx22 3 4 3 13 Evaluate a b d c 14 Evaluate each limit a Find the acceleration a t b When is the object traveling the fastest c Find the distance traveled in the first 2 hours 16 Find the derivative of each function 17 Find the nth derivative of 18 Find the 43rd derivative of 19 Evaluate 15 The velocity of an object is given by miles per hour t is in hours d At what value of t does the graph of D t the distance traveled in t hours have an inflection point xxxx 22limxxxx 2lim0xxxee5237lim xxxee5237lim xxbxxaxx1sinlim 5tan2sinlim 22040 8 5 tttv 5 tan 1 3 2 42232xxfcxxxfbxexfax xxxxfcxexfbexfa2 2 3 xxxfcossin 2082514 35 kkkbka 20 Find the right hand left hand and midpoint Riemann sums using n equal subintervals for the given function interval and n Sketch the function and the rectangles on the interval 2 4 n 4 Evaluate 21 Find each antiderivative 22 Evaluate each definite integral a b a b c d e f c 9 2 xxfnnR lim3 0 1 on 8 2 nxfx dxxsin xdxxcos3sec22dxxx 3 1 dxxxxex153 dtttt tan secsec dxxx16522dxxxebdxxax 303021154 9 dxx 2321211
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