For the function y = (x² + 4)(x³ − 9x), at (-3, 0) find the following. (a) the slope of the tangent line (b) the instantaneous rate of change of the function

Q: the cost (in dollars) of producing x units of a certain commodity is c(x)=100+50x-0.02x^2 (a) Find…

A: Given, the cost function C(x)=100+50x-0.02x2 a) The average rate of change of the function from…

Q: 17. y = x – 2x3 x = 3 Δx = = dx – 0.001

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Q: (3) Evaluate the definite integral 3.5 (a) √2²5 √7-2xdx

A: As per the company rules, we can solve the first question and rest can be reposted.

Q: Given the curve r(t) = (cos 3t, sin 3t, 2t) Find the following unit vectors and simplify your final…

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Q: Find the arclength of the curve r(t) = (7 sint, -3t, 7 cost), -6 ≤ t ≤6 PESUGIHAK

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Q: If a rock is thrown upward on the planet Mars with a velocity of 19 m/s, its height above the ground…

A: Topic- application of derivatives We are given,Height of rock above the ground (in meters ) after t…

Q: lim h0 lim ho ((x + h)' - x3 h √x +h=√x h

A: a). The given limit is: limh→0x+h3-x3h

Q: What is the slope of the tangent line to x³-2xy³-y²= -5 at (-2,1)? Select one: O a. 1 O b. O c. -1 O…

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Q: Question Determine the intervals over which the function shown below is continuous. Enter your…

A: To determine the intervals over which the function shown below is continuous.

Q: Consider the following. f(x) = (x (x² + 4x + 4)(x-4) (a) Find the derivative of the function, and…

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Q: Fencing a Field Consider the following problem: A farmer has 2400 ft of fencing and wants to fence…

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Q: A particle moves along a straight line with e velocity speed f(t) = 15 + 48 t + 1 m/s m/s

A: Oh

Q: Let G(x) = = - 7x + 12 |3 - x| + |x-1| for x = 3.

A: The given function, Gx=x2-7x+123-x+x-1 for x≠3 We have to simplify the function Gx on the interval…

Q: f(x) = x - 4; g(x) = Determine k so that f(x) = g(x), for all x. A. -8 B.-4 k if x=-4 if x = -4 C.4…

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Q: Find the domain, range, intercepts, symmetries and asymptotes of the following function 1. y = x³

A: 1. y=x3 Since you have posted multiple question in this question which are not interlinked so i have…

Q: Comet Craig-1959 moves along an ellipse with equation 49x² + 4y² - 196 = 0 (shown below) -10-9-8-7-6…

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Q: The tables below show some inputs and outputs of functions f and g. -8-5-1 1 5 12 2 -2 -10 -24 f(z)…

A: This question can be solved using the concept of composition of function.

Q: On one production line in a small custom chip factory, marginal costs decrease rapidly as more chips…

A: x= Number of chips in thousands. c(x)= cost in hundreds of dollar. Given that c'(x)=10x It costs…

Q: Find the derivative of the function. 3 2 + X g(x): = X + 93√x

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Q: Consider the following. 1 - 2x² x42x² + 3 Let u(x) = 1 - 2x² and v(x) = x² − 2x² + 3. Find each…

A: We need to find derivative.

Q: 17. lim x² + 3x

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Q: The graph of y = f(z) is shown in blue. Draw the graph of y = f(2), shown in red, by determining how…

A: Given Graph:-

Q: Consider the initial value problem For what value(s) of y, will the solution of the ivp have a…

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Q: Find the average rate of change of the function f(x) = -x² − 8x - 12 on the interval - [−3, −3 + h].…

A: Average rate of change of change of f(x)  on [a, b] is  m=fb-fab-a

Q: The graph of he following function has on horizontal tangent line with equation f(x)=x√²

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Q: What is the equation of the tangent line to f(x)=3e²x+cos4x at x = 0?

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Q: Find the complete solution: dy dx c and m are constants - my = cemx

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Q: Evaluate the limit. 2³ +1 lim 1+1 (x + 1)³

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Q: y = f(x) N.K. X -1- (a) lim [f(x) + g(x)] (b) lim [f(x) = g(x)] - (c) lim [f(x)g(x)] -1 y 1 y = g(x)

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Q: Consider the following. 0.4 6.0.4. +2 √4-25x2 dx

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: Determine the intervals over which the function shown below is continuous. Enter your answer in…

A: Consider the function

Q: The revenue function for a sound system is R(x) = 200x - x² dollars where x denotes the number of…

A: Topic - Application of derivatives We are given, Revenue function :R(x)=200x-x2and  we know that…

Q: given f(x) = 3x2 + 2x + 11 and found f '(x) = 6x + 2.   (a) Find the instantaneous rate of change of…

A: Given f(x) = 3x2 +2x+11

Q: XT f(x)=8+x+tan ( -). Find f-¹(f()). Round/truncate your answer to three decinal places.

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2- Find the range of f(x) = √√x² - 4.

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Q: The logistic growin P(t) = is used to model population growth, where Po is the initial population at…

A: Given : P0=1500K = 1000r0=0.1P=90%P=0.9P=0.9*1500=1350

Q: Find an equation of the tangent line to the curve at the given point  *please use handwriting not…

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Q: (Technology Permitted) The population P of wild turkeys in a sanctuary is given by P(t)=et+2 5+1500,…

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Q: IF The Following vectors are be equal A = 21-î+ (27_1) E B = 2X² +47 +3K Find The Values oF (X.)

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Q: If I know the characteristics of the graph of a sinusoidal function, how can I write an equation for…

A: If I know the characteristics of the graph of a sinusoidal function, then to explain how can I write…

Q: 3 22. Find f if f"(x) = 20x² + 12x² + 4 f(0) = -10₁ f(1) = 8 f(x)=

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Q: B/ Represent the plane (2, 4, -6), the top line locates in this plane, the point B(1, ?, 2) locates…

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Q: If f(x) = 8x², find: f(4+h)-f(4):

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Q: (a) lim [f(x) + g(x)] X-2 (b) y y = f(x) y = g(x) A. K X lim [f(x) = g(x)] (c) lim [f(x)g(x)] f(x)…

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Q: QUESTION 3 Let f(x)=√x x and g(x)=x² Find gof(x) and state its domain.

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Q: 1 Let f(x) ƒ(x) = = . Find f-¹(x) - 01 Ox 1

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Q: Let f(x,y) = x²-3x 1+x²y² a) Find the first and second partial derivatives. of f by hand. b) Find…

A: Note:- according to the company policy we can solve maximum three subpart so please upload the next…

Q: The Graph below represents the velocity of a particle moving on a horizontal line on the interval…

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Q: 05 Comparing Ay and dy In Exercises 13-18, use the information to find and compare Ay and dy.…

A: The formulas we use: △y=f(x+△x)-f(x) dy=f'(x)dx d(kxn)=knxn-1, k is a constant