) (a) (b) (c) Differentiate y == the function by using rules. 1 2x - 3 y = ln(7x + 5) y = 3x³e5x

Q: Two fire-lookout stations are 14 miles apart, with station B directly east of stat notation is N35°F…

A: Let the position of fire be at C. Given, Distance between two fire lookout stations AB= 14 miles…

Q: Calculate the derivative using Part 2 of the Fundamental Theorem of Calculus. d dx re¹2x d dx x4…

A: This question can be solved using the concept of fundamental theorem of calculus part 2 according to…

Q: 7. Integrate the following indefinite integrals. 3e5x dx 1-2e5x a.

A:

Q: 20. Find curl(F), where F(x, y, z) = xyz¹i+x²zªj + 4x²yz³k. a) (-4xyz³)j + (xz¹)k b) x²yj+xz¹k c)…

A:

Q: Given f(x) = 2* cos x, 0 ≤ x ≤ í, find the critical point(s) on the given interval. If necessary,…

A: Answer :   Critical point : x = 0.193π and increasing in nature.

Q: If -2 5 [° f(x)dx = [__ * f(x)dx + [_^¸ ƒ(a)dx − [¯* f(x)dx, -8 what are the bounds of integration…

A:

Q: What is the explicit equation for the nth term of the arithmetic sequence 6, 3.5, 1,-1.5, 4,...?…

A: We have: a1=6 -- the first term   Next, we calculate the common difference d=a2-a1 So, we have:…

Q: Determine for the following function: dy dx y = log3 (x² + 1) ○ (z²+1) In 3 2x O (1²+1) 2x O 2x…

A:

Q: Which of these equations represents a line that is perpendicular to the line in the graph below?

A: Two lines are perpendicular if the product of their slopes is equal to -1

Q: Differentiate y = (2x³ + 3x² - 1)5 5(6x² +6x)4 30x(x+1)(2x³ + 3x² - 1)4 30x(x + 1)(2x³ + 3x²-1) O…

A: The given function y=2x3+3x2-15 we have to find the derivative of the function

Q: 4. Identify the focus of A. (0,3) -(y - 3)² = (x-2). B. (4,3) C. (2,1) D. (2,5)

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Q: The slope for a horizontal line would be which one of the following?

A:

Q: Which of the following is an example of an inequality? 60 + |-3| = 63 60 + 2x < 120 60 - 2(15) =…

A:

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cose

A: The given function is : s(θ)=200sinθcosθ We need to find the derivative in two ways.

Q: Consider the graph below and determine the open intervals on which the function is increasing and on…

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Q: Find the absolute maximum and the absolute minimum for the function f(x)=e−x−e−5x,…

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Q: What is the domain of the rational function(x)=-3x²-16x +48 Oxe 31x*-4,-2.3.4) Oxe 31x*-4, 3, 4) O…

A:

Q: How do you indicate an 'or equal to' inequality on a graph for a 2-variable inequality? By using a…

A:

Q: The marginal revenue from the sale of x cans of air freshener is given by 4.4 -0.32√x dollars per…

A: In here, the marginal revenue is given as a function of x. So, we will use the formula: Marginal…

Q: Find the Fourier series for the following functions: {3¹ f(x) -2≤x≤0 0≤x≤2

A: Given functionf(x)=-1     if   -2≤x≤03        if       0≤x≤2

Q: 5.f 21 dv (v-1)(v+3)(v-4)

A: We can evaluate the given integral by using the partial fraction method.

Q: Solve the system of equations eie= cose -isin (0) in(e) is the imaginary unit and is the base of the…

A: Given system of equations eiθ=cosθ+isinθe-iθ=cosθ-isinθ

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Q: Inequalities can appear in which of the following types of equations? Rational equations and linear…

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Q: -5 2 y=f" (x) A description of the graph of f(x) would be: a 4th degree polynomial a downward…

A: There is a given linear graph representation of second derivative f''(x) of a function as f(x). We…

Q: 3 Find ( + 6x + 2) dr + C

A: To evaluate the integral.

Q: 1 3 2 + To find the blue shaded area above, we would calculate: b ľ f(x) dx = area Where: a = 2 3 4…

A:

Q: (i) Consider the function f: R\{-2,3} → R defined by 2x³4x²5x - 3 x²-x-6 f(x)= - (a) Prove, using…

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Q: I. Find the solution set of the following. 4. cos ¹(2x) + sin¯¹ √√1 − 4x² = π

A:

Q: The critical numbers r = -1 and x = 2 are found from a continuous derivative f(x). Given that the…

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Q: Prove that lim 12 √16x +9y¹2 2 6 4x² +3y does not exist by showing that the limits along different…

A: We have to prove that  limx, y→0, 0 16x4+9y124x2+3y6 does not exist.

Q: Find the sum 3n

A: Given: ∑n=1∞n2+n3n

Q: Evaluate the definite integrals using properties of the definite integral and the fact that 5 5 S √³…

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Q: Define the force field F(x, y, z) = (xy, —-yz, xz). Find the divergence and curl of F. Let C be the…

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Q: Find the exact arclength of y = 2x3 for 0≤ x ≤ 2:

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Q: 7. y - y = 16

A: The objective is to find the general solution .

Q: 1 cos³x -dx =

A: The given integral is 1/Cos3x.

Q: If [ 2013 |檳 sin ada = −a³ cos x + 3x² sin x + k fæ sin ædæ, find k d. 3/2 a. 6 b. -3/2 C. -6

A:

Q: what does the following integral equal? L 9(2)dz - [ = ['s g(z)dz = 23 and g(z)dz = 6.5

A: Given:             ∫-9-1gzdz=23              ∫-4-1gzdz=6.5              ∫-1-4gzdz=-∫-4-1gzdz

Q: hat is the average rate of change of f(x) = ln(x+4)/2x+1 over each interval? Give the answer…

A: Given: f(x) = ln(x+4)/2x+1 (a) [-1, 8] (b) 3.45&lt;=x&lt;=5.25

Q: A function is given below. Determine the average rate of change of the function between t = 6 and t…

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Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

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Q: Differentiate y = √x + √z 01 O 2√x+1 A+ 2√x + 2√x O 2√x + √x

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Q: 4. Determine the maximum point of the the graph of y = 1 — 2 sin(π – 2x), for x = € [−π, π). 3.

A: Let's find maximum points of trigonometric function.

Q: 76°F Partly sunny -6-5-4 -3-2 y range 6 5 4 X = 3 2 1 (a) Find h(-2), h(0), h(2), and h(3). h(-2) =…

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Q: On Integration of Rational Fractions. Distinct linear linear factors ³+3x+1 8) (x+1)²(x-2)²

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Q: [2 2x log 2x dx

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Q: III. Consider the power series +∞ n(3x + 2)n n³ +4 n=1 -1. 1. Show that the series is absolutely…

A: Given power series is ∑n=1∞n(3x+2)nn3+4 When x=1, the series becomes…

Q: What is the equation of a line with slope of 2 and a y-intercept of -6? y = -6x + 2 y = 2x - 6 2x…

A: Concept: The equation of a line is found using the slope-intercept form of a straight line. We need…

Q: The base of a solid is the region in the xy-plane between the the lines y = x, y = 4x, x = 1 and x =…

A: