Sπ/4 x² dx (x²+4)5/2 (Use trigonometric substitution)

Q: Explain why you think the sequence -2, 25 125 " ... 8 2 32' . converges to a finite number or…

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Q: Exercise 5 Find the center of mass of the uniformly dense upper half disk x² + y² ≤ R², y ≥0. Your…

A: Solved below

Q: To evaluate S (In x)² -dx, apply integration by parts twice. For the second application of…

A: Follow the procedure given below.

Q: log(x+3) z-1-1-cosh(cos-12) 4. lim

A: Given,            limx→1-log12x+31-coshcos-1x

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A: At first, we will do partial fraction then we will do integration

Q: Find the area of region bounded by the graphs of the equations. a. X b. y = x + sin x y + 3 2 1+ -R…

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Q: 1 x√x²-2x =dx : √x²-2x x =+c C

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Q: Find the derivatives of the function xy² x-y x + y

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Q: e falling parach

A: answer is in next step

Q: Using trigonometric substitution, what is √x²-9dx ? f x3 A sec (-) √x²_9 6x² +C B ¹ (1) - V +C (ⒸC)…

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Q: 2b. Explain the difference between a partial derivative and a directional derivative.

A: Dear learner, as per our guidelines we can provide the solution for one part only. Kindly post other…

Q: Question 8 Let f(x) = (z - 6)² Find a domain on which f is one-to-one and non-decreasing. Find the…

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Q: π/2 sin (cos() sin() dx (Consider initially the first 2 terms)

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Q: 8 x²-1 x³+x A. -1 dx = √( + g(x)) + g(x) a dx, then A + f C. 1 g(x) dx is c B. -1 + In(5/2) to D.…

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Q: Evaluate the definite integral. Joe²¹i+ i+e¹j+t kdt kat O © 2²² ² x i 2 © (e²-1) e² O e²-1 2 O e²…

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Q: 1. ) cos (4) COS -π/2 f/² sin (1) sin (²) dx (Consider initially the first 2 terms)

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Q: [sin³() cos(4) dx (A B C) D 32 32 3/² cos (4) + 3 cos (4) + C 5 32 3 cos (4)[-5cos² (4)+7] 35 32 35…

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Q: y = 1 V25-x2

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Q: 1. ² sin() cos() sin(x) dx (Consider initially the first 2 terms)

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Q: a's father is planning to open a savings account to pay for Amelia's college education. He has found…

A: Given query is to find the value of deposited amount.

Q: In the following graph draw the vectors v = [0, 3, 1] and w = [0, 1, 4]. (a) Highlight the…

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Q: Find the average value of the function over the given interval and all values of x in the interval…

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Q: dx 1+tan x

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Q: II. Find Do not simplify your answers. dy da tan ¹(cosh x) 2. y= (sin² x) (sechar)sec z [use…

A: Given data÷

Q: rem, if applicable, to determine if f(x) takes the value 0.1 for some x in [0, 1].

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Q: Find the domain of the vector functions, r(t), listed below. using interval notation. 1 a) r(t) =…

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Q: Find f'(1) given that f(x) ax+b cx+d' where a, b, c, d are constant.

A: we have to find derivative.

Q: Find T(t) and N(t) at the given point. T(0)=(1,1,1) N(0) = (0, 2, 1) x = e cost, y = et sint, z=e¹;…

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Q: Find the antiderivative F(x) that satisfies the given condition. F'(x) = 4ex - 5x²; F(0) = 10

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Q: Find E (p) for the price demand equation and interpret the results. x = f(p) = 1200(50p) where p-$28…

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Q: Write 20 terms of the Fibonacci sequence

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Q: S sin (Inx) dx? How many times will you perform integration by parts to evaluate

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Q: 1 sinx+cosx+1 -dx

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Q: x²√√2x-x² dx

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Q: Given the function C(a) = (x-4) (x + 6) (x - 1) its C-intercept is its x-intercepts are

A: Solution is given below:

Q: 8. The integral What is the value of A. B. can be rewritten as 15x²x³43x - 19 (x + 1)²(x² - 6x +13)…

A: Let's find.

Q: x²+x+1 Sa 2x²+2+3+x A B cb dx g(x) - dx = [Aƒ (x) − B ln(g(x)] + D fb da, and if A = ‚B <0, then dx…

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Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 6 in.…

A: A box with a square base and no top is to be made from a square piece of cardboard by cutting 6 in.…

Q: x²+x+1 so Ja 2x²+2+x²+x dx dx = [Aƒ (x) – B ln(g(x))] à + D fb +2 and if A=,B<0, then g(x) = .

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Q: Question 4 Solve the equation: 1²+t+19-0. Fully simplify all answers, including non-real solutions

A: The given equation is: t2+t+19=0

Q: 14. Evaluate the following √x-²sec (+)tan ³ ( =) « dx 2tan (²) [7tan² ( ² ) +11] +C 77 2tan…

A: To evaluate: I=∫x-2sec41xtan521xdx Substitute 1x=t⇒-1x2dx=dt⇒x-2=-dt So, I=∫sec4t  tan52t…

Q: Consider using the method of partial fractions to solve x²+x+1 rb Sa 2x²+2+x²+x - dx = [Af(x) – B…

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Q: Using trigonometric substitution to solve: f sin 2x +C 8 cos x√3-cos²x 1 + C 8 secx√4-sin²x sin 2x…

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Q: Find a set of parametric equations of the line through the point (1,-2, 3) and perpendicular to the…

A: Concept: As we know that a equation of the line through the point (α,β,γ) and perpendicular to the…

Q: Find the arc length of the parametric curve. L x = 4 cos(t), y = 4 sin(t), z = 3t; 0≤t≤ T

A: Given problem:- Find the arc length of the parametric curve.   x = 4cos(t), y = 4sin(t) , z = 3t ; 0…

Q: Find the integral: x+2/x-1 dx choices: a) x+ ln(x-1)3+C b) x+ ln(x-1)2+C c) x+ ln(x-1)4+C d) x+…

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Q: Solve the system x' = 22+2y y' = -4x+8y-4z = 2z with initial conditions, r(0) = 5, y(0) = 7, and (0)…

A: We use the Laplace transform to solve the given system

Q: A hot air ballon is hovering 83 meters above the ground and begins to assend at a rate of 9 meters…

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Q: Given the function f(n) = 3n¹ +33n³ +90n²: its f-intercept is its n-intercepts are

A: We can find the intercepts as below in the following steps.

Q: sin³ (cos(4) dx 2 32 Ⓒcos A COS 35 32 B 35 32 Ⓒ-3 cos (4) C 32 D 3/7/7 C (4)[-5cos (4)+7] 5³ (4)…

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