Calculus question and answers for January 13, 2024
- Q Find the partial derivative indicated Assume the variables are restricted to a domain on which the function is defined z sin 7x y 4xy
- Q Suppose f x y xy 3 Compute the following values f 5 4 f 4 5 f 0 0 f 2 4 f x 5 f 4 y f t...
- Q 6 To reach Platinum Medallion status with Delta Airlines you need to fly at least 75 000 miles but less than 125 000 miles in a given year Express the...
- Q 7 Kalia is planning the transportation for the senior trip The number of students in the senior class is 463 but the trip is entirely voluntary If each bus can...
- Q 9 Use algebraic and interval notation to describe all possible values of a so that 2 81
- Q 10 Which of the following statements is true about the set of real numbers described by the interval 15 1 A This set contains only one point x 15 y...
- Q 8 If you spend more than 50 at Old Navy shipping is free Let s be the total amount spent at Old Navy Use algebraic notation to describe all possible...
- Q YA 9 8 7 6 5 1 1 y f x MA Nigh y g x 2 3 4 5 6 7 89 EXAMPLE 4 Using graphs to evaluate composite...
- Q Find the equation of a line tangent to the curve xy xy x 1 at the point 1 2 OA y 5 667 2 667x OB y 2 x OC...
- Q 7 10 points The following figure shows the level curves of z two variables P where fr is positive Q where fr is negative 0 R where fy is zero...
- Q 21 32 Find the derivative of the function using the definition of derivative State the domain of the function and the domain of its derivative 21 f x 3x 8...
- Q 3 A rechargeable battery is plugged into a charger The graph shows C 1 the percentage of full capacity that the battery reaches as a function of time elapsed in...
- Q 2 10 pts Define your variables translate the following information into a system of linear equations and then solve the system Write your answer as a complete sentence Two rainstorms...
- Q 1 2 Use the given graph to estimate the value of each derivative Then sketch the graph of f 1 a f 0 e f 4 b f 1 f...
- Q f x is continuous for 0 5 x 0 2 and also has the following values X f x 0 5 0 4 0 3 0 2 1 1 1...
- Q 3 Match the graph of each function in a d with the graph of its derivative in I IV Give reasons for your choices b YA VA I III YA...
- Q The acceleration m of an object along a straight line is given in the following graph sec2 Acceleration 10 5 1 0 1 Time OA 53 5 meters OB 28...
- Q Given that g is the inverse function of f and f 3 4 and f 3 5 then g 4 O A B O C 3 5 O E 3...
- Q 17 For the function g whose graph is given arrange the follow ing numbers in increasing order and explain your reasoning 0 g 2 g 0 g 2 g 4...
- Q If q is positive and increasing for what value of q is the rate of increase of q twelve times that of q A 3 OB 4 5 OC 2...
- Q Using a left endpoint Riemann sum approximation with four equal subintervals the approximate value of fo g x dx is A 8 B 8 C 16 OD 16 01 2...
- Q 5 10 points A function f x y is differentiable and satisfies f 2 1 3 fr 2 1 0 5 f 2 1 5 Find the equation of the...
- Q 3 The displacement in meters of a particle moving in a straight line is given by the equation of motion s 1 1 where t is measured in seconds Find...
- Q D a Find the slope of the tangent to the curve y 2 x at the point where x a b Find equations of the tangent lines at the points...
- Q 4 12 points Let f r be a scalar valued function of a single variable r satisfying f 0 df Define a function dr 2 f 0 1 where f...
- Q If the function f has a continuous derivative on 0 c then ff x dx A f c f 0 B f c f 0 C f c D I...
- Q Let f x x 9 X 6 g x X X 6 Express f x g x as a rational function f x g x for x Simplify your answers...
- Q Find the first and second derivatives d dx y 29 x 29 x d 2 dx 29 x
- Q Describe the domain of the function g x 1 6 x The domain of the function consists of all real numbers x where Type an inequality
- Q X 9 x Let g x h g x 1 h x x3 3x 8 Calculate the function h g x
- Q Find an equation of the line such that the points An equation of the line containing the points Type an equation 5 and 3 4 4 are on the line...
- Q Differentiate y X x 2 2 x dx 2 11
- Q Let f x 7 X a Find the derivative f x b Find f 2 1 a What is the first step in finding the derivative of f x 7...
- Q 6 If f x X find f x h f x and simplify f x h f x
- Q If f x x 5x find f 0 f 4 f 5 and f 8 f 0 Simplify your answer f 4 Simplify your answer f 5 Simplify your answer...
- Q Determine whether the following limit exists Compute the limit if it exists x 3x 4 X 4 lim X 4 Is the function f x x 3x 4 X 4...
- Q Let f x x 8 h x 4 4x Calculate the following function f x h x f x h x
- Q Factor the following polynomial 4x 32x 64 4x 32x 64
- Q a Find the slope of the tangent to the curve y 2 x at the point where x a b Find equations of the tangent lines at the points 1...
- Q a Find the slope of the tangent line to the parabola y x 3x at the point 1 2 i using Definition 1 ii using Equation 2 b Find an...
- Q 15 42 Find the limit or show that it does not exist 4x 3 x 5x 1 15 lim 3t t 3 t t 4t 1 17 lim 1118 rr...
- Q 3 For the function whosc graph is given state the following a lim f x b lim f x x18 x118 c lim f x x 1 e The equations...
- Q The quadratic formula is used to solve for x in equations taking the form of a quadratic equation ax bx c 0 b b 4ac 2a Solve for x in...
- Q If dx 1 x xy x 0 and y 4 when x 1 when x 3 y OA 2 381 OB 4 711 OC 3 898 OD 3 898 OE...
- Q 2 a Can the graph of y f x intersect a vertical asymptote Can it intersect a horizontal asymptote Illustrate by sketching graphs b How many horizontal asymptotes can the...
- Q If the graph of y X C asymptote x 2 then b cannot be equal to A 0 ax b B 7 O C 5 OD 12 O E 10...
- Q 1 Explain in your own words the meaning of each of the following a lim f x 5 818 b lim f x 3 8118
- Q The rectangle shown below has vertices of 0 0 0 2 1 and 0 1 y cos x What percent of the rectangle is shaded OA 63 7 B 36...
- Q A particle moves along a line so that at time t where 0 t its position t is given by s t 4 sint 10 What is the acceleration of...
- Q If y 2 f g x then y O A f g x g x B g x g x O c 2f g x g x D 2 g...
- Q If y 2f g x then y A f g x g x B f g x g x c 2f g x g x D 2 g x g...
- Q Which of the following will not give the instantaneous rate of change of f x with respect to x when x 3 f 3 f 3 0 1 0 1...
- Q What is the minimum value of f x 3xe OA 3e OB 338 e O C 1 D 0 E f x has no minimum value
- Q Given the values of f x shown in the chart below which of the following could be values for f x at x 11 212 and 3 X 1 2...
- Q Given that f 0 5 2 and f 0 5 4 using a tangent line approximation you would estimate f 0 to be A 0 B 3 OC 2 D...
- Q A 17 m Using trapezoids estimate the total distance the runner travels from t 0 to t 6 seconds B 12 m C 24 m D 26 m t seconds...
- Q The graph of which of the following equations has y 1 as an asymptote O A y sin x B y In x 3 2x OC y 2x 13x 7...
- Q A puppy weighs 2 0 pounds at birth and 3 5 pounds two months later If the weight of the puppy during its first 6 months is increasing at a...
- Q The velocity of a particle is shown in the graph below For which x values would the acceleration of the particle be zero Click here for long description OA x...
- Q limx o e In x x3 O A OB O C 1 OD O E 1
- Q X y The sides of the rectangle above increase in such a way 1 and da d 3d At the instant when x 4and y 3 what is the value...
- Q The absolute minimum value of f x x 3x 12 on the closed interval 2 4 occurs at x OA 4 OB 2 O C 0 O D 1 OE...
- Q Consider the function x whose graph is composed of two intersecting line segments shown below Which of the following are true for f x on the open domain a c...
- Q If f x sin there exists a number c in the interval x 3 that satisfies the conclusion of the Mean Value Theorem Which of the following could be c...
- Q Water is pouring into a container at a rate given by ri t t gallons hour water is pouring out of the same container at a rate given by ro...
- Q The graph of y is concave downward for all values of x such that A x 2 OB x 0 O C x 0 OD x 2 OE x 5
- Q If fis a differentiable function f a is given by which of the following lim 0 f a h f a h f x f a limx a x a...
- Q The region enclosed by the curve y ex the x axis and the lines x 0 and x 1 is revolved about the x axis Find the volume of the...
- Q 4 The function 7 x has the value J 1 dy the expression 2x 1 y 1 dx The slope of the curve at any point is A Write an...
- Q An equation of the line tangent to the graph of f x x 1 2x at the point 1 1 is A y 6x 5 B y 2x 1 C...
- Q If the function f is continuous for all real numbers and if f x x 2 then f 2 A 0 B 2 C 1 D 4 E 2 x...
- Q 2 In this problem you will investigate the family of functions h x x cos ax where a is a positive constant such that 0 a 4 A Graph the...
- Q Note t 0 corresponds to midnight Time is measure in hours and the rate of water usage is measured in millions of gallons per hour Rate millions of gallons hour...
- Q The tank s base diameter is 40 m and a height of 10 m A Write an expression for the rate of change of the water level with respect to...
- Q 5 The figure at right is the graph of f x the second derivative of a function f x The domain of the function f x is all real numbers...
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