Write an equation of the form y= a sin bx or y= a cos bx to describe the graph below. 'y 3 AA x -2 4 6 -2 -3

Q: √x x² ln x dx

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Q: Sketch the region enclosed by the curves à - 5 = 4y and x − 21 = (y — 4)², and compute its area.

A: x-5=4y⇒x=4y+5     x-21=(y-4)2 ⇒x=(y-4)2+21 Area between the curves…

Q: √x² +16 dx

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Q: the

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Q: 4. f cot³ 2x csc¹ 2x dx = f cot² 2x csc4 2x cot 2x dx = f(csc² 2x - 1) csc* 2x cot 2x dx Let u =…

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Q: The fixed overhead expense of a manufacturer of children’s toys is$400 per week, and other costs…

A: Let's find.

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Q: ∫ sin4x dx

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Q: In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 45 +…

A: Solution of given question is written in below steps.

Q: Question 15 Find the derivative of y = 32x+5 A. 2 ln 3 (3²x+5) B. In 3 (3²x+5) C. 2ln 3 D. 32x+5 O B…

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Q: Find the rectangular equation of the curve given by the parametric equations below. Then graph the…

A: The given parametric equation,   x=t2, y=-2t

Q: Find T(t) and N(t) at the given point. r(t) = 7 cos(t)i + 7 sin(t)j; t = 3 T() 3 N(₁) 3. =

A: Given, r(t)= 7cos(t)i+7sin(t)j We know that,…

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A: Area above x axis is positive  are below x axis is negative ∫02 gt dt  = area from 0 to 2=16∫24 gt…

Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x - y³ dy=0 is

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Q: Use the given derivative to find all critical points off, and at each critical point determine…

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Q: f(x) = loga x

A: ddxlogax

Q: A rectangle has its two lower corners on the x-axis and its two upper corners on the curve y = 4 -…

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Q: ∫ (1 + secx)2 dx Evaluate indefinite anti-differentiation

A: Solve it

Q: d d alculate ——[r₁(t) · r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt he product…

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Q: s x3 √1-x² V dx

A: Given: I=∫x31-x2dx   ...1   As we know that; The Power rule; ∫xndx=xn+1n+1+C

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Q: Find the critical number of the function defined by f(x) = x² + 4x O-1 and 0 are the critical…

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Q: x²+x-1 dx 5x² + x3-x

A: First we take partial fraction then solve it.

Q: [₁ 2x - x² dx

A: To integrate.

Q: ∫ sinx √cosx dx

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Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A: We have to find the surface area.

Q: Identify and sketch the graph of the equation in R³. Identify and sketch the graph of the traces as…

A: An equation is given                         -x+y2+z29=0We will name and sketch the graph of the…

Q: ∫12v (7+6v2)9 dv Evaluate indefinite anti-differentiation

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Q: 2. Write the given (total) area as an integral. (3 points each) a. The area above the x-axis and…

A: area

Q: Find the equation of the tangent line to the graph of f(x) = x'e- at x = 0.

A: The given function is f(x)=x9e-x at x=0.

Q: (8x4 − 5x2 + 2)dx evaluate indefinite anti-differentiation

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Q: State the coordinates of the intercepts, stationary points, and the inflection point of p(x) = 2x³ -…

A: Here we have to use the concept of derivatives

Q: The concentration of a certain drug in the bloodstream t minutes after swallowing a pill containing…

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Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j + tk; t = T() 6 37 0, √/3 X N…

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Q: f[in (w) ² ] ^ 4 3 dw

A: ∫lnω24ωdω=∫2lnω4ωdω=∫16ln4ωωdω=16∫ln4ωωdω Substitute u=lnω⇒dudω=1ω⇒dω=ωdu; 16∫ln4ωωdω=16∫u4du…

Q: A 6 inch by 6 inch piece of cardboard has square cut out of its corners so that it can be folded up…

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Q: Scos2x (2 2 Cos 2X (2 cos 2X -1) dx

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Q: s sin² (3x) cos³ (3x) dx Hint: cos²x = 1 - sin² x 07 sin²x = 1 - cos² x

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Q: 3 4d³y - 13d +6y=0 dy dx3 dx

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Q: Find the sum of the series, if it converges. Otherwise, enter DNE. 6 Σ n(n + 2)

A: Given problem:-

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C' is oriented counterclockwise.…

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Q: √25x2-4 -dx, 2/5 cosø dø 2/5 sec^2 ødø 2/5 seco tanø dø None of the choices

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Q: pt) Given the following geometric sequence: Get an expression for an Evaluate So Evaluate So if…

A: Geometric sequence

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Q: The figure in this exercise shows a horizontal layer of the vector field of a fluid flow in which…

A: This is a problem related to vector field. Based on the formula and concept we will answer the…

Q: Recall that the Maclauren series expansion for f(x) is given by f(n) (0) r. Find the Maclauren…

A: The function is given by fx = ex Tp evaluate: The Maclauren series of the function fx.

Q: Find the extreme values of on [-2,2]. f(x) = ret, x < 0 2x³9x² - 12x, x ≥ 0

A: Solution of given question is written in below steps.

Q: ∫(√(cos(x)) (sin^3 (x)) dx) what is the answer to this integral?

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Q: Calculate the derivative. g" (0), g(s) = es S+7 (Give an exact answer. Use symbolic notation and…

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Q: a. b. ² (30e³P +/- ¹ dp р 4 1 2 2x4 dx

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