Given f(t)=(3t^2-1)i+4tj+(14-t^3)k, , find the unit tangent vector and a set of parametric equations for the line tangent to the space curve at the point (11,8,6).

Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = 180x + 3x2² - 2x³ (a) Find…

A: Since first two subparts are already solved , i solved the third subpart

Q: The derivative of a function f(x) at x = a is given by √√1+h-1 h lim h→0 Find f(x) and a. f(x) =

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Q: (A) f'(x) = (C) f'(x) = e+e-> (e-e) (e +e¯)-(e² −e¯¹) (eª +e¯²) (e+e-)2 (e +e-)²-(e-e¯¹) ² (e+e-)² =…

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Q: 1. If g(x) = -1x¹/3, find g(-27).

A: Question no. (1):If , then to find .Note: Since the student has posted multiple questions and does…

Q: Find by implicit differentiation. dy dx dy dx || X sin(y) + y sin(x) = 8

A: given information

Q: Let f(x)=√71-x The slope of the tangent line to the graph of f(x) at the point (7,8) is The equation…

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Q: X y = e sin(x)

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Q: A farmer has 225 yards of fencing to form two identical rectangular pens and a third pen that is…

A: A farmer has 225 yards of fencing to form two identical rectangular and a third pen that is twice as…

Q: d) lim √2-x X-2+ 4 e) lim (¹2) x-3x-2

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Q: Find an equation of the tangent line to the curve below at the point (0, 1). 2 1+e- y = y=

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Evaluate the integral using partial fraction method J (3x²+2) dx (x + 2) (x² + 4)

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Q: 3. Differentiate the following functions and state whether they have maxima or minima. a) y =…

A: Note:-Since you asked multiple questions which are not interlinked, according to our policy we can…

Q: Find the derivative of the function. f(0) = cos(8²) f'(0)

A: We have given We have to find the derivative of the given function.As we know from chain rule that…

Q: Find at æ = 3 if y=-5x² - 2 and da dt dy dt = 4.

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Q: Write an equivalent integral with the given order of integration a = b 2 2-1 x [² ²² ² F(x, y, z)…

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Q: 23. y = In x+1 x-1

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Q: Intervals of Increase and Decrease and Local Extrema Answer the following questions using the…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 1. (a) f(0) = ln(sin 0) + sin(ln). (c) y = ln |x³ - x²| Find the derivative of each function. (b)…

A: Note:-Since you asked multiple sub parts questions , according to our policy we can answer only…

Q: Use logarithmic differentiation to find the derivative y = (cos x)ª²+1

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Q: Find the four second partial derivatives of f(x, y) = 7x+4y7 +6x6y5. 224 2

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Q: Consider the function ƒ(x) = 7(x − 2)²/³. For this function there are two important intervals: (-∞,…

A: f(x)=7(x−2)2/3

Q: For the following function, a) give relative minimum, or neither; b) identify intervals where the…

A: k(x)=3x4

Q: Find the RREF of the matrix -4 1 -3 من که من 2 3 -1 4 -2 3 2

A: to find the row reduced echelon form of -4       31      - 1-3       42       - 23        2

Q: Given the function graphed below, evaluate the definite integrals. -1 0 4 3 2 1 -1 -2 -3 -4 1 f(x)dx…

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Q: If xy + 5ey = 5e, find the value of y" at the point where x = 0. y" =

A: xy+5ey=5e

Q: 10-- 8 4 2 y 8 ► » -2 2 4 6 8 10

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Q: Find dy/dx by implicit differentiation. ex/y = 9x - y y (9y-¹) y²-xexv Enhanced Feedback

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Q: 1. Compute the following limits. sin(2x) 6x (a) lim x→0 5√x x+0+ sin(8√x) cos² (x) - 1 x (b) lim (c)…

A: Apply L'Hopital's rule.

Q: Given that answer = 4 11 f(x) dx = 45 11 what is [ 11 f(r)dr?

A: int 4^11{f(x)dx}=45/11

Q: K Find the first and second derivatives. 6 X dy dx y = 5x-5 11 d²y dx² ||

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Q: cos(x2) 2. Find the derivative of 2 +1

A: (2) y=2cos⁡(x2)ex+1

Q: 27. y = x²(1 - In x²)

A: To find the derivative of the following function.

Q: One-to-one? One-to-one? Explanation Check 864 6-4-2- 864 2 4--6--8-0 Yes O No + 2 Graph 4…

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Q: Let f(x) = {(x²-1) x²-x+k₁ ifx <₁; ifxzi kan find the limit of f(x). (1) lim, ₁- f(x)= 1 (ii) lim +…

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Q: Find an equation for the line with slope m = -6 and which goes through the point (-5, -1). Write…

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Q: A 5 m ladder leans against a wall. The bottom of the ladder is 1.3 m from the wall at time t = 0 sec…

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Q: Differentiate the function. h'(x) h(x) = n(x + √√x² − 3) -

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Q: The integral in this exercise converges. Evaluate the integral without using a table. 50⁰ 0 3dx (25…

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Q: Draw and label a diagram to help solve the related-rates problem. The side of a cube increases at a…

A: We consider a cube on each side is x m long.Draw a cube and mark its length, width and height as x m…

Q: x²dy+(y²-xy)dx=0

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Q: |zx − 8x|u[ = h (³)

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 1 2 3 2 a 1 1 To find the blue shaded area above, we would calculate: ·b [ f(x) dx = a Where: 1 f(x)…

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Q: converging on a single point as they fly at right angles to each other. One plane is 304 miles away…

A: Air traffic control detects two airplanes at the same altitude converging on a single point as they…

Q: A manufacturer of tennis rackets finds that the total cost C(x) (in dollars) of manufacturing x…

A: We first find the profit function.

Q: Problem #6: For which of the following can we use intermediate value theorem with the interval [a,…

A: The objective of the question is to check which functions are eligible for using the intermediate…

Q: Utilize the definition of the derivative to prove that (sinx) = cos x

A: To prove (sinx)' =cosx using the definition of derivative.

Q: 6. Find y" for the curve cosa-siny = 4.

A: Given .We know,

Q: Answer using the following polynomial using remainder theorem. Show your solutions. f(x) = 4x5 -…

A: To answer the following polynomial by using remainder theorem.

Q: The linear approximation at a = 0 to sin(4x) is A + Bx where A is: and where B is:

A: We need to find the linear approximation of  at

Q: Differentiate the function. f(x) = 260 f'(x)

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