Each of the following questions carries the stated number of marks. Write your answers in the space provided. Show full working. f(x) = 1-x, x < 0 a+bx+ 2x², x ≥ 0 f(x) is both continuous and differentiable on R. Use the definitions of continuity and differ- entiability to determine a and b.

Q: Find the derivative of the function at Po in the direction of A. f(x,y) = -5xy-y², Po(7₁-7), A=2i+3j

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Q: Let f(x, y, z)=xze +3(x+y)-xz³. Then the derivative off in the direction of v=7+j+2k at the point…

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Q: Find the producers' surplus for the supply curve p = 0.02x + 7 at x = 100. O $800 O $100 O $200 O…

A: The producer surplus formula is given below.

Q: If k(x) = 249(z) and k(4) = 2, then k' (4) = 8 ln(2) - 1 8 ln(4) +1 O-8 In (2) + 1 ○ In (2) + 1 0¹ 4…

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Q: Flight of a Rocket The altitude (in feet) of a rocket t s into flight is given by s = f(t) = -t³ +…

A: s=f(t)=-t3+54t2+460t+6

Q: x)=-2x7/4+28x-13 What are the critical values of the function - separate multiple answers with…

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Q: A graphing calculator is recommended. Determine the end behavior of P. P(x) = x4 − 7x2 + 2x + 4

A: End behavior of a function is where the function tends when x tends to -infinity and +infinity.

Q: Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and…

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Q: Find the equation of the elipse

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Q: Show all steps for each part of the curve sketching algorithm clearly, number each section in your…

A: y=-12x2-4x3

Q: Evaluate the integral. (Use C for the constant of integration. Remember to use absolute values where…

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Q: Which of the following statements is true? Responses The series ∑n=1∞(−1)n+11n√ diverges by the…

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Q: 1. Eliminate the cross-product term by a suitable rotation of axes a. x² + xy + y² = 6 b. 3x²…

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Q: Triangle ABC has vertices A(4, 7, 7), B(1, 6, 5), and C(–2, 9, 8). Which kind of triangle is △ABC?…

A: given  A=(4,7,7) B=(1,6,5)C=(-2,9,8)distance between two point is D=(x2-x1)2+(y2-y1)2+(z2-z1)2

Q: Maximize the value of the function A=4xy subject to x + 2y = 24. DO NOT answer any of the following…

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Q: The period of a pendulum (the time elapsed during one complete swing of the pendulum) varies…

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Q: Find the linear approximation L(x) of the function f(x) = √4 - x at a = 0.

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Q: A family is taking a trip. During the first 3 hours, they travel at a rate of 45 miles per hour.…

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Q: Differentiate the following functions using the power rule. Use positive exponents in each final…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Question 3 cos(0)= Given A B с D -21 5 -8 | 5 7 25 = 16 25 1 <0- 5 and <<, what is the value of…

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Q: List the critical numbers of the following function in increasing order. Enter N in any blank that…

A: s(t)=6t4+8t3-12t2for crtical numbers put s'(t)=0d dt(tn)=ntn-1

Q: If 900 square centimeters of material is available to make a box with a square base and an open top,…

A: As we know that Volume of the box = Area×height For largest volume , either dVdx = 0 or dvdy = 0

Q: The height s (in feet) at time t (in seconds) of a silver dollar dropped from the top of a building…

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Q: Refer to the graph of f shown in the following figure. 6- 5 4+ 3+ 2+ 1 0 1 2 3 4 5 6 7 8 9 10 11 12…

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Q: Find an upper bound for |ET| in estimating O 10 5 64 25 S (2x3+5x) dx with n = 10 steps.

A: ∫-142x2+5xdx

Q: Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable.…

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Q: aw Əw at w=f(s³ +1²) and f'(x) = ex. Find - and at əs

A: Given that the two variables function

Q: - sin(1-1) inches per hour, where t represents hours since 12 a.m. The water level of a certain body…

A: As per rule I need to solve only first three subparts.

Q: Find the volume of a pyramid with a square base, where the perimeter of the base is 4.7 cm4.7 cm and…

A: We need to find volume of pyramid for given data.

Q: The points at which a quadratic equation intersects the x-axis are referred to as:

A: We have to find what the points are called at which a quadratic equation intersects the x-axis.

Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. 1/128…

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Q: Evaluate the limit In(t + 6) t - 10 -i + 10t²j + (t + 6)²k) lim t→0 Enter your answer in i, j, k…

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Q: b) c) f(x) = (4x² − 3)(x − 6) g(x)= x²+7x x+6x-1

A: To find the derivative of the following functions. (b) fx=4x2-3x-6 (c) gx=x3+7xx2+6x-1

Q: Suppose dy/dx=2x(x^2+3)^2 and y(0)=2. what is y(2)?

A: given dydx=2x(x2+3)2 y(0)=2we know  ∫xndx=xn+1n+1+c

Q: Suppose dy/dt= 6 ze^(3z^2+2) and y(0)=4. what is y(1)?

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Q: A javalina rancher wants to enclose a rectangular area and then divide it into five pens with…

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Q: The figure shows a sector of a circle with a central angle 0. Let A(0) be the area of the segment…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: D Question 11 O 175m Find the volume of the solid generated by revolving the region about the given…

A: The region in  the first qushant bounded above by the line y=5. below by the line y= 5x/3 and on the…

Q: Find a unit vector in the direction in which f(x, y) = 8 - x² - y² decreases most rapidly at…

A: f(x,y)=8-x2-y2

Q: (b) Find the total area between the graph and the x-axis between x = -2 and x = 1. Round your answer…

A: (a) To select the correct graph of fx=xx+2x-1. (b) To find the total area between the graph and the…

Q: Use a linear approximation (or differentials) to estimate the given number. (Use the linearization…

A: We have given the number 1/99. Since 100 is near integer of the value 99, choose the value a = 100…

Q: Consider the following. 8 dt Find the indefinite integral and set up the limit that will be used to…

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Q: Sketch the region of integration, reverse the order of integration, and evaluate the integral. 1/4…

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Q: Find the derivative of y with respect to t. y = cot¹√6t

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Q: Write a recursive rule for the sequence. a_(n)=3n-7

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Q: You are given the graph of a function f. 0 concave downward 1 Determine the intervals where the…

A: You are given a graph of a function f. To determine the intervals where the graph of f is concave…

Q: Use cylindrical coordinates to find the volume of the region bounded by the plane z = √29 and the…

A: The region bounded by the palne z=29 and the hyperboloid z=4+x2+y2

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)= - 8x²8xy-8y²…

A: Given function is

Q: Select the expressions that are equivalent to 7(q+5)

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Q: 0 K A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 900…

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