Calculate the length of the path over the given interval. (sin 7t, cos 7t), 0≤t≤n

Q: Find all values of a where the given series converges. Answer: Note: Give your answer in interval…

A: Value of x for which series is convergent is given.

Q: Find all solutions of the equation in the interval [0, 21). csc 0 7 3 If there is more than one…

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Q: If In a 2, ln b = 3, and ln c = 5, evaluate the following: = (a) In (10-2) = b-4c² (b) In √6-³c-²a-1…

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Q: An open box is to be made out of a 12-inch by 14-inch piece of cardboard by cutting out squares of…

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Q: Ex. (9) Solve 3y"-2y' + y = 4x+2

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Q: Consider the function f(x) = S3x³ eºdt. a) Apply Part 1 of the Fundamental Theorem of Calculus to…

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Q: Find the limit. 3 lim x-6 5x + 2

A: we have to find limit

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 2√x + √x dy Read It Need…

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Q: 2. y = tan-¹(cosh x) (sin² x) (sech x) secx [use logarithmic differentiation]

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Q: Write the Taylor series for f(x) = sin(x) at x = Find the first five coefficients. Co C₁= C2= C3=…

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Q: dx secx+1

A: First simply the equation Using Trigonometric identities.

Q: 1) fx-²dx 2) sin(n)dx

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Q: Locate the absolute extrema of the function on the closed interval. f(x)= x³ 12x, [0, 4] -

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = -2x - (sin(x))² dy= Need…

A: Using derivative

Q: Suppose parametric equations for the line segment between (7,-3) and (8, 2) have the form: Т a + bt…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Show that the lines L₁ : x = 4-t, y = 2t, z = 1+ t and L₂ : x = 1 + 2t, y = 3 - 4t, z = 5 – 2t are…

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Q: More on Areas. Farmer Jones, and his wife, Dr. Jones, both mathematicians, decide to build a fence…

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Q: (a) Find the acceleration of the body each time the velocity is zero. Enter your answer as a list if…

A: Follow the procedure given below.

Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

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Q: Find the radius of convergence of the power series. (If you need to use co or -00, enter INFINITY or…

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Q: Solve the following differential equations of d²y dy dx² +==X dx

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Q: Given the function f(x) = -√√x + √³, find f'(6). Express your answer as a single fraction in…

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Q: Sketch the region enclosed by the curves and find its area. y = x, y = 3x, y = -x + 4

A: Given; y=x, y=3x, y=-x+4   Now find the point of intersection between the line y=-x+4 & y=3x.…

Q: Convert the rectangular equation to polar form. xy=14

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Q: (-3,0) (0, -1) (-1,-2) y = h'(x) (0, -2) (3,0) c

A: Given problem:- Suppose that h(x) is continuous everywhere, with the graph of h'(x) given on the…

Q: 5. (a) Find the exact value of sin (20) given that sin (0) = 3/5 and 0 is in quadrant II. (b) If cos…

A: Given problems:- 5. (a) Find the exact value of sin (2θ) given that sin (θ) = 3/5 and θ is in…

Q: Locate the absolute extrema of the function on the closed interval. f(t) = ₂, [3,5]

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Q: Solve xy = 8y - 3x, y(1) = −1. (a) Identify the integrating factor, a(x). a(x) = (b) Find the…

A: xy'=8y-3x

Q: Evaluate the line integral ſ F. dr, where F(x, y, z) = sin x i + cos y j + xz k, where C is given by…

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Q: Graph the pair of parametric equations with the aid of a graphing calculator x = 4 sin t - sin 4t, y…

A: Given x=4sint-sin4ty=4cost-cos4t0≤t≤2π

Q: What are the cylindrical coordinates of the point whose spherical coordinates are (3, 5, 1)? r = 0 =…

A: Given: spherical coordinates ρ,θ,φ, here ρ=3,θ=5φ=π6 To find : cylindrical coordinates r, θ, z

Q: interval of convergence = 0

A: Follow the procedure given below.

Q: 6- Given the function below -(x+1) ²+7 X2

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Q: ☎ Q1: If x=² and y=21³ then b) 3 314 ² dx d) at x=4 F others Choose

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Q: How many terms of the series do we need to add in order to find the sum to the indicated accuracy?…

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Q: Find the exact length of the curve x = tsint, y = t cost where 0 ≤ t ≤ 1.

A: answer is in next step

Q: Find the Maclaurin series and corresponding interval of convergence of the following function. f(x)…

A: Let's find.

Q: II. Find an equation of the plane containing the points (0,2,-1) and (1,-1,-1) and perpendicular to…

A: we have to find the equation of plane.  Let, a,b c are the direction ratios of required plane 1.

Q: 8 sin 8. Then sketch the curve.

A: The correct curve of r = 8 -8sin(θ) is  Option (C)

Q: The conic section whose equation is x2 - 3y2 - 8x + 12y + 16 = 0, is ______. centered on the origin…

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Q: Evaluate the following limits. USE OF L'HOPITAL'S RULE IS NOT ALLOWED. 3. lim (x-3) tan(9-x²) sin²…

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Q: Find the domain and range of the function graphed below. 5+ 3 -5 -4 -3 2 1 2 3 4 5 Domain: Range: ON…

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Q: Find the volume of the solid obtained by rotating the region under the graph of the function f(x)…

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Q: Write the Taylor series for f(x) = eª about x = 1 as Σcn(x − 1)". - n=0 Find the first five…

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Q: Do as indicated. 2. Use the Squeeze Theorem lim sin (sinh x)csch x. x-18 to evaluate

A: Given problem:-

Q: the

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Q: Find the volume of the th

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Q: Find T(t) and N(t) at the given point. π r(t) = 4 cos(t)i + 4 sin(t)j + tk; t = 2 4 1 T(+7) = -√17 Т…

A: given  as you have already found Tangent vector

Q: Find the value k that makes the function continuous. kx 10, x 10 M > f(x) = _ 4x + 10, x < 10 Submit…

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Q: If f f(x) dx = 12, then ff(4x) dx is equal to If f f(x) dx = 12, then fx f(x²) dx is equal to

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