Calculus question and answers for August 20, 2023
- Q Find the slope of the tangent line to the curve3x xy 2y = 160at the point ( 4, 4).-
- Q The function f(x) = 6x +9- has one local minimum and one local maximum.This function has a local maximum at x =_____with value______and a local minimum at x=____with value________
- Q 1as follows: Let f(x)1.001CUse linear approximation, i.e. the tangent line, to approximateand find the equation of the tangent line to f(x) at a "nice" point near 1.001. Then use this...
- Q Use the chain rule to find the derivative of f(x) = 3ef'(x) =4-975
- Q 33. Sketch the graph of a function that satisfy the following conditions:f(0) = 0, f continuous and even. f'(x)=2x if 0<x< 1, f'(x) =-1 if 1<x<3 and f'(x) =1 if...
- Q The circumference of a sphere was measured to be 84 cm with a possible error of 0.5 cm. Uselinear approximation to estimate the maximum error in the calculated surface area.Estimate...
- Q Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate In(1.28).L(x) =In(1.28) ~
- Q Use Newton's method to approximate a root of the equation 2x + 3x + 3 = 0 as follows.Let x? = 1 be the initial approximation.The second approximation x? isand...
- Q A rotating light is located 12 feet from a wall. The light completes one rotation every 3 seconds. Findthe rate at which the light projected onto the wall is moving...
- Q A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speedof 6 ft/sec along a...
- Q 5. Suppose f is continuous on [0, 4], f(0) = 1, and 2 Sf'(x) ? 5 for all x in (0, 4). Showthat 9? f(4) ?21. (Justify your work).
- Q A room contains 8 people, each of a different age. The people leave the room in random order, one at a time. What is the probability that they leave the...
- Q A 9-digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the remaining 8 numbers. How many telephone numbers are possible in which all...
- Q Given thatf (x) =2(3-x)(x+4)(x-1)Solve the following inequality f(x) ? 0Include the following information:The boundary points and the multiplicity of eachThe intervals. The sign(positive or negative) of the rational expression in...
- Q f(x)=-3x+2xg(x) = 2x+3Find f-g and fg. Then, give their domains using interval notation.(f - g)(x) = []Domain of f - g :(f*g)(x) =Domain of fig
- Q Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = -4 and g'(2) = 3. (Enter your answer as...
- Q Find the magnitude and the direction of theresultant vector.(-6, -2) wA. 8.06, 60.26B. 19.42, 34.51C. 8.06, 29.74D. 19.42, 55.50?(10, 9)
- Q Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile inthe shape of a right circular cone whose base...
- Q The cost of a trip is $3.15 plus $0.95 for every kilometre that you ride on a bus.Which of the following expressions gives the cost of a trip of &...
- Q dyUse implicit differentiation to find given the equation sin(xy) = y5.dx
- Q If the tangent line to y = f(x) at (4, 2) passes through the point (0, 1), find f(4) and f'(4).(4) =f'(4) =
- Q Let F(x) = f(x) and G(x) = (f(x)) .You also know that a = 6, f(a) = 3, f'(a) = 6, f'(a) = 3and G'(a) =Then F'(a) =
- Q (10 points) A ladder 10 m long is leaning against a wall. If the base of the ladder is sliding away fromthe wall at the rate of 1 m per...
- Q (10 points) A spherical balloon is inflated so that its volume is increasing at the rate of 20 cubic cm persecond. What is the instantaneous change in surface area, ds...
- Q An oil spill is pouring oil onto a sea in the shape of a circle. The slick is growing at arate of 150 m2/s.How fast is the radius changing when...
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