the vector-valued function.

Q: Find the limit of the trigonometric function. lim 9 sin(x)

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Q: Find a power series representation for the function. (Give your power series representation centered…

A: We have to find the Power series representation.

Q: Use the following binomial series formula to obtain the MacLaurin series for ∞ (a) (1+z) k=0 (b) √ 1…

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Q: 1 - √xdx

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Q: A 10,000 litre rainwater tank is to be built in the shape of a cylinder. It must be at most 3 metres…

A: As per our guidelines we can answer only 3 subparts of the given equation. Kindly repost the…

Q: For the given vectors a and b, find the cross product a × b. a = (1, 0, -3), b =(3, 4, 0) axb=

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Q: Find r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). ● r(t) = 2t²i - 2tj + = t³k (a) r'(t) (b) r"(t)…

A: Let's find.

Q: The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) dy

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Q: Homework 11 Parametric: Problem 5 Given ze and y = tet, find the following derivatives as functions…

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Q: Solve the D.E ý - y = x لم

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Q: X (b) lim 0 DO (c) lim xln 1

A: (b). Given: limx→0+lnxx

Q: dx 3xy 10. Find for xy = In (cos x + sin y) by using implicit differenti dx 1. Find dx for y³ + 4x…

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Q: Use the Product Rule to differentiate the function. f(x)= x cos(x) F'(x) =

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Q: Find r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). ● r(t) = 2t²i - 2tj + 53³k (a) r'(t) (b) r"(t)…

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Q: Find the exact length of the curve given by Length = x = 2t², y = (0 ≤ t ≤ 4).

A: A detailed solution is given below

Q: Use the form of the definition of the integral given in this theorem to evaluate the integral. [²4x³…

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Q: VI. Write TRUE if the statement is correct, otherwise write FALSE. There is no need to justify your…

A: Find your answer below

Q: A particle is moving with the given data. Find the position of the particle. a(t) = 3 cost-2 sint,…

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Q: Find an equation for the conic that satisfies the given conditions. parabola, focus (5, -3), vertex…

A: The general form of the parabola is given by: y=a(x-h)2+k...(1) where (h,k( is the vertex of the…

Q: Find the arc length L of the graph of r(t). L = r(t) = 11 cos(t)i + 11 sin(t)j + tk, 0≤t≤ 2π

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Q: Find the limit. lim t→3(t i-4 j + t² k) a z→3(t 1-4 j + P²³ k) = [i i+ Mi + M k

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Q: 17. Let y = 4t² + 3, t = 6es and s = 1 + In x. Find in terms of x. dx 18. Given y = 5t (3 - t), t =…

A: Let's find.

Q: 2. Evaluate the following (Express all answer in Rectangular Form): d. √9+ 2i e. 2¹ + ln(2 + i)

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Q: -10 -10 8 61 0

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Q: Sketch a right triangle corresponding to the trigonometric function of the acute angle 8. sin(8) - 1…

A: Using the properties of trigonometric functions we find the given values

Q: Replace the polar equation r = 5 csc 0 with an equivalent Cartesian equation. Then identify the…

A: The given polar form of the equation is: r=5 csc θ

Q: Sketch the region bounded by the graph of the equations and find the area of the region. 1 y = y =…

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Q: Representing a function as a Power Series. Suppose that we want to represent the function f(x) =…

A:

Q: the

A: We will solve the Differential equation.

Q: Let f(x)=x2+2x-1 and g(x)=2x-4. Find 3f(x)-2g(x)

A: Given fx=x2+2x-1 & gx=2x-4 To find 3f(x)-2g(x):

Q: A metal plug has been designed using the intersection of the two cones z = √√x² + y² and √x² + y² +…

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Q: 2 Find az/ax if the equation yz - Inz = x + y

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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: [√x (x - 5)dx

A: ∫xx-5dx∫xx-5x dx∫x32-5x dx

Q: Evaluate the ff. limiti. Uning of "L'Hospital' rule is not allowed lim √1-x + 2x + 7 x>-∞ √√9x²+5 -…

A: To evaluate the following limits without using L'Hospital's rule.1 limx→-∞ 1-x+2x+79x2+5-32 limx→1…

Q: 4. sinx 1-sin² x dx

A: integration

Q: Find the nth Maclaurin polynomial for the function. f(x) = ex, n = 5 P5(x) =

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Q: I sold something on ebay and I go to the UPS store to ship the package. The cost for the box is $3,…

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Q: Activity 1.3. B Evaluate the limits of the following functions. 3. lim (ex + 2) -X+0

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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: A B D Find the area, A, of the region enclosed by the cardioid r = 8 + 8 cos 0. 96 л 52 t 48 100 π

A: First I have written the area formula for polar curve , then draw the graph of given curve and then…

Q: Change the polar equation 2r = 2 + cos 0.(2r - 1) to Cartesian equation

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Q: e3x-6-2, [2x - 5], √x²-9, if x ≤ 2 if 2 3

A: answer is in next step

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = e, y = 1…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find the indefinite integral. (Use c for the constant of integration.) [₁4 (4t³i + 14tj - 6√tk) dt

A: Here we have to use the concept of the indefinite integration.

Q: 3. Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that has a…

A:

Q: Is the output true or false, I need the output step by step and a clear line please al = 25 dB al =…

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

Q: Use the formula k(t) k(t) = ||r' (t) x r"(t)|| ||r' (t) ||³ = r(t) = e³ti + e-tj to find k(t).

A: By using the formula kt=r't×r''tr't3 to find kt.rt=e3t i+e-t j