Find a vector v with initial point (-4, 0, 3) and terminal point (-3, 5, 7). Then find a unit vector in the direction of v. You don't have to make the little arrow things on top of the vectors you can just use the letters ,j,k.

Q: Find the distance from the point (0,1,-1) to the line a(t) = (-2, 2, 4)t + (-6, - 1,5)

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Q: Given f(x,y,z) = x²y³z+ye -√4-x², find the first order partial derivatives f₁, f, f

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Q: Calculate the mean, median, and mode from the following data set: 1,2,3,4,5

A: The objective of this question is to calculate the mean, median, and mode of the given data set.…

Q: if f(x)= 5 sin to the negative one power ( x to the thrid power) then what is f prime of x

A: The objective of the question is to find the derivative of the function f(x) = 5sin^(-1)(x^3). This…

Q: Find f'(x) and simplify. f(x)=7׳ (x² -9)

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Q: Find к for the space curve r(t)=(12 sin t) + (12 cost) j +9tk. K(t)=[ (Type an exact answer, using…

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Q: Find f'(x) and simplify. f(x)=2x5(x-9)

A: Given that the expression we have to find the derivative of the given expression

Q: Write an integral that represents the area of the shaded region for = cos(20) as shown in the…

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Q: (a) How many one-to-one functions are there from a set with four elements to a set with five…

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Q: Find the length of the indicated portion of the curve. r(t) (3e cost) + (3e sint)j+3e'k. - In4sts0…

A: Given:To find:The arc length is calculated as-

Q: Need to use the horizontal line test to determine whether the function is a one -to -one and sketch…

A: Need to use the horizontal line test to determine whether the function is a one-to-one and sketch…

Q: horizontal asymtotes of  1 (x−3)2

A: The objective of this question is to find the horizontal asymptotes of the function 1/(x-3)^2. A…

Q: A company manufactures a units of one item and y units of another. The total cost in dollars, C, of…

A: We solve the given problem using the second derivative test.The Second derivative test :Let f(x) be…

Q: Find the derivative of the following function from first principals: Y - - 1 X

A: To find the derivative of the following function from the first principle.

Q: can you solve this question for me

A: The objective of this question is to determine whether the given series converges or diverges. If it…

Q: Use the given information to find the exact function value. Simplify your answer as much as possible…

A: Given that the expression

Q: Let ā = - -71 – and 6 = −41 – 57. Find a. b -

A: Required answer is 33Explanation:

Q: A certain electronics manufacturer is making GPUs for gaming laptops (GPU stands for graphics…

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Q: Use integral tables to evaluate the integral. Sx√29x-7dx Click here to view page 1 of the Table of…

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Q: I need help with this

A: Magnitude of all three required complex numbers are 52​Explanation:Approach to solving the question:…

Q: Simplify cot (17) - t) to a single trig function using the 2 sum or difference of angles identity.

A: given

Q: (d) Horizontal asymptotes. (e) Intervals where f is increasing and decreasing. (f) Local minima and…

A: Given: To Find: To determine the following: (d) Horizontal asymptotes(e) Intervals where f is…

Q: Complete the parametric equations of the line through the point (4,3,1) and parallel to the vector…

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Q: Consider the piecewise function x, -2 0. (v) Find the simplified general expression for the Fourier…

A: The objective of the question is to analyze the given piecewise function f(x) and determine its…

Q: Find two unit vectors orthogonal to both u: (no decimals). unit vectors = = (3, -2, -1) and v = (0,…

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Q: f(x) and (f'(x))² into the surface area equation above to find b Surface Area = Lº 2π. = a 5 5 2π…

A: To explain how was the 2 used from 2pie. How is it determined the 2 is needed, when in other cases…

Q: The derivative of the [Select] of two functions is the first times the derivative of the second,…

A: Consider that have two functions and . The product rule states that:where:- and are the two…

Q: Find the following limits

A: The final answer is:The limit does not exist.Explanation:

Q: Find the area of one petal of r = 9cos30

A: r=9cos⁡3θFor the area of one petalr=0cos⁡(3θ)=03θ=−π2,π2θ=−π6,π6−π6≤θ≤π6

Q: (9x8 - 2x - 6) dx

A: The given integral is

Q: A polar curve is given by r = 5 (3-cos(e)) What is the slope of the tangent line to the curve at 0 =…

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Q: The Taylor series

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Q: 3) An adult human at rest inhales and exhales approximately 520 ml of air (called the tidal volume)…

A: Question No. (d):Given: An adult human at rest inhales and exhales approximately 520 ml of air…

Q: Vector-valued functions (VVF) VVF Point P t value (for point 1 r(t) = ½ t²i + √4 − t j + √t + 1k (0,…

A: equation of tangent is as follows-2x​=−22​1​y−2​=23​1​z−1​Explanation:Step 1:Step 2:Step 3: Step 4:

Q: Estimate the area of the surface generated by revolving the curve y = cos(2x), 0 ≤ x ≤ x-axis. Use…

A: y= cos(2x)n=3

Q: #8 Find the average rate of change of n(x) = √√x-1 from x = 5 to x = 10. SHOW ALL WORK!

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Q: Solution to question 2 (a),(b),(c) please

A: (a)f(x)=arcsin(log2​(2x+1)+x)f′(x)=1−(log2​(2x+1)+x)2​3​⋅(2x+1)ln(2)+11​ (b)…

Q: Given the series: 1 1 k k+3 k=6 does this series converge or diverge? diverges converges ×

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Q: Let f(x, y) = x³y and c(t) = (t², t³) (a) Calculate: Vf. c'(t) = (b) Use the Chain Rule for Paths to…

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Q: Let ā = (5, 1, −1) and ỗ = (2, 1, 4). Find a. b.

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Q: 1. f(x) = (4 — x²)5

A: Second derivative test for local maxima and minima :

Q: 135. Evaluate sin x sin x + cos x sin x dx in two ways: dx, then using the Evaluation a. By…

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Q: Find f'(x) and find the value(s) of x where f'(x) = 0. f(x)=2 X x +36

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Q: Use sigma notation to write the sum.

A: Answer is 4Σn=1 = [1-(n/4)2]Explanation:Step 1:Step 2: Step 3: Step 4:

Q: Csc (2x)-2=o Four smallest solutions

A: Given that the equationcsc(2x)-2=0 we have to find the solution

Q: Find four intervals on which f is one-to-one, making each interval as large as possible. Four…

A: Given graph of function f(x) to find the intervals on which f is one to one

Q: Suppose that ƒ is a function given as f(x) = −x² + 5x − 3. Simplify the expression f(x + h). f(x+h)…

A: given function

Q: Find the points of intersection of the graphs of the equations. Ө r= and r= 1.8 1.8 Select one: O a.…

A: The correct option is (d). (1 . 8 , 3.24).Explanation:Step 1:To find the point of intersection…

Q: For f(x)dx = lim f(x," )Ax,, determine the value of Axi. √²₁₂ max Ax, 0 Ola n 21˚ O O n 4-0 O O >18

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Q: 2. Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: The equation of  the tangent line to the curve x2+2xy−y2+x=20 at the point (4,8) is…