Find the arc length L of the graph of r(t). r(t) t L= = ³²³i + 1 j + 1/2 √√61² k, 25157 = i

Q: 11. Given the function below, what is its derivative? * f(x) = 2x - √x f'(x) = 2x C f'(x) = 2 - a 1…

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Q: 3. x³ = x + 2y x-2y " y'

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Q: The equation below gives parametric equations and parameter intervals for the motion of a particle…

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Q: Question 10 Given: y = xcos (x); Find y'". O(E) None of these Oy" xsin (x) + 2 cos(x) Oy" asin (x) -…

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Q: 1. f(cos 3x - x²) (sin 3x- x³)5 dx 2. f cos² x (tan x) (sec² x − 1) dx 3. f tan x (sec² x - 1)(sec²…

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Q: Given: y = (In x)" (In x)", find dy/dx.

A: The given function,     y=ln xx

Q: 2. Let f be the function from {a, b, c, d, e} to {1,2,3,4} with f(a) = 3, f(b) = 1, f(c) = 2, f(d) =…

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Q: Question 8 Find the derivative -[f (x)] dx Anmospace support = 3 In (In (x²-3x + 5)²) 3(2x - 3)…

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Q: \1/2 2. y = (2 tan² 20-1)

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Q: PH Given: = ln(x²y-1); Find dy/dx.

A: Given xy=ln(x2y-1)

Q: The f sin 2x cos 2x dx is 1+3 cos 4x 1 sin²4x + C 24 1 In|1 + 3 cos 4x| + C 12 {A} {B} {C} - In|1 +…

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Q: y = 2-ex 3x-1

A: We know that differential power rule is given as - d(xn)/dx = nxn-1.   Here i attached the solution…

Q: Determine a for each arithmetic sequence. See Example 5. 33. as = 27, as 87 www 34. α12 = 60, 920 =…

A: A detailed solution is given below

Q: Σ n=2 7 n(In(n))*

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Q: Show that the Differential Equation is EXACT and then solve it. 2. (cos2y - 3x2y2)dx + (cos2y-…

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Q: The f xcos x² 1-sin x2 dx is

A: Given :

Q: Consider the function f that is continuous on the interval [-5, 5] and for which ſo f(x)dx = 4.…

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Q: Evaluate the following integrals. 2. √x* +5x³+ x+5x³+20x+16 x(x²+4)² dx

A: Solving

Q: 8. For the enclosed regions bounded by y = x² - 6x and y = -2x in the graph, what is the integral…

A: Given   From the graph intersection point

Q: For the following: a) Determine the intersection points. b) Draw a sketch of the graph. c) Find the…

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Q: 5. Use spherical coordinates to evaluate [[[ (x² + y² + 2²) ² dv D where D is the solid hemisphere…

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Q: Evaluate the iterated integral. 8 4 b²b²x + (x + y) dy dx

A: Given query is to find the value of the integral.

Q: 6. Evaluate any 5 of the following 6 integrals. (a) 12 dx 1 (b) (c) cos(50) de (e) [x²e² dr (d) (f)…

A: To evaluate the following integrals.d ∫xx+1 dxe ∫x2ex dxf ∫arcsin x dx

Q: Comput: f dx 2+x

A: I am attaching image so that you understand each and every step.

Q: Find the present value of a $45, 000 annual income stream if it is invested immediately as it is…

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Q: Solve for dy/dx and simplify the result y = (5x + 2)6 (3x² +7)7

A: As per our guidelines we can only solve one question and rest of the question will be reposted.

Q: 8. Sketch the curves and determine the area of the region formed in the given interval: y = √√2x, y…

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Q: 7. Determine each of the following for the function, f(x, y) = 7x³y² - 2x + 3y. Show all ^~^ints.…

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Q: 0 if t 5 Find the Laplace transform, F(s) of f(t) F(s) = ķ

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Q: lim (t i − 4 j + t² k) 1-9 ■im (t i − 4 j + t² k) = i →9 i+ i

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Q: Find the answer to the application problems. 5. If v(t)=t²-7t+10 represents the velocity function of…

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Q: | 12 – 2 – 1 2x - (x − 1)²(x² + 1) dr

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Q: f(x) = 1x4 + 1⁄2x³ 3x² +5 f(x) 20 15 10 W -8 -6 -4 2 4 6 -5 -10 -15 -20 Determine intervals on which…

A: Given query is to find inflection points.

Q: 4. r(x) = 3x) (1 - x)(-/-)

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Q: 32 Question * (3 Points) The proper transformation for sin²x to make the f sin²x dx readily…

A: substitution

Q: Using Variable Separable, solve x² (y + 1) dx + y² ( x − 1) dy = 0

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Q: y = tan 2x 1-cot 2x

A: Given,            y=tan2x1-cot2xTo find : Find the derivative of the given function.

Q: dy Find given that dt x² + y² = 2x + 4y, x = 3 y = 1, and dy = | dt dx dt = 6

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Q: a. f(x) = on [-1,4] 1²+2 b. f(x) = I√4-1² on [−1,2] c. f(x) = 2 sec r - tan r on [0,1]

A: At the  extremum of a function f(x), the first derivative is zero.

Q: Evaluate the iterated integral. 6 (x + y) dy dx Jo Jo

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Q: The base of a three-dimensional figure is bound by the line y = √x + 2 on the interval [-1, 1].…

A: We have to find the volume of bounded region in the interval [-1,1].

Q: Consider the curve C with parametric equations given below, defined for t ∈ R. (a) Determine the…

A: We use the properties of parametric curve

Q: C. Find the angle coterminous to the given angle that has the opposite sign. бл 1. - 7 2.-258°

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Q: A. Indefinite Integrals + C. Evaluate the following integrals. dx x + x3 1 Ans. In x² 1 + x²

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Q: Find the partial derivatives f(x,y)=e* sin(xy) of dx

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Q: * Find the derivative lic F (+) = (+³-2+ +1) (2+²

A: Given query is to find the derivative of the expression.

Q: D Question 5 Find the derivative of -2x f(x) = x f'(x) = -2x²e-2x (E) None of these f'(x) = e-2x…

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Q: Consider a triangle ABC like the one below. Suppose that A= 116°, C=36°, and a = 19. (The figure is…

A: A triangle ABC has A=116°, C=36°, and a=19

Q: x²-3x - 7 √(x² + x + 2) (2x - 1) dx

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Q: the following 2 √x² √₁ + x dx aluate

A: Given query is to find the integral.