Consider the following scenario. Suppose you start at the point (0, 0, 8) at t = 0 and move 10 units along the curve x = 8 sin(t), y = 6t, z = 8 cos(t) in the positive direction. Using the given parametric equations, give the corresponding vector equation r(t). r(t) = Find r'(t) and Ir'(t)\. r'(t) = |r'(t) = Find your location after moving along the curve as described. (x, y, z)=(

Q: Q15 Find all non-zero derivatives of the following function: f(x) = 5x³ - 7x² + 9x - 1

A: Here we differentiate f(x) with respect to x until it becomes a constant

Q: Sketch the region of integration and convert the polar integral to a Cartesian integral or sum of…

A: Please see the below picture for detailed solution.

Q: Given ƒ"(x) = 6x – 5 - and ƒ'(−2) = −1 and ƒ(−2) = 2. Find f'(x) = and find f(2)=

A: We need to find out the value of f'(x) and f(2) for which the second derivative is given.

Q: Solve the differential equation. 2xy + 4x + (x² - 4) dy dx = 0 =

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Q: Find √ √1 + x²dx

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Q: In evaluating 2₁3² (x³ – 1) ¾ dx, we make the substitution u

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Q: Find the volume of the pyramid with base in the plane z = -10 and sides formed by the three planes y…

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Q: Consider the function ƒ(x) = x¹ − 18x² +8, −2 ≤x≤7. This function has an absolute minimum value…

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Q: 3. Use the Gizmo to experiment with more functions of the form y = b*. Select the Show probe and…

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Q: Find the area of the surface obtained by rotating the curve y = √2x from x = 0 to x = 7 about the…

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Q: At exactly two of the labeled points in the figure below, which shows a function f, the derivative…

A: Given graph:-

Q: distance in between the point P(3, 1, 2) and the point Q(0, 4,

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Q: (a) Find the derivative. y = In(4x - dy dx (b) Find the derivative. y = ln ( 4x = dy dx 6) - 3 In(x)…

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Q: (a) Find the linear approximation L(x) of 2 f(x) = x³ at x = 3 L(x) = x = 27. (b) Use L(x) to…

A: The given function fx=x23. To find the linear approximation of fx at x=27.

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

A: On finding the limit of the given sequence we will check the given sequence is convergent or…

Q: 4. Consider the graph to the right, containing the points (0, 1) and (1, 5). A. What function is…

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Q: . Evaluate the limit for the graph: lim f(x). |y4 4 a. 3 b. 2 2 -4-20 2 -2 -++-% x c. d. 5 does not…

A: We will find the required.

Q: 14. The domain of the function is y 4 2 -4-20 2 4 x

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Q: Find the limit. lim X→0 sin (8x) 7x

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Q: 17x³ (In x)² dx =

A: The given integral is: ∫17x3 ln x2 dx

Q: The tangent to (2,4) on the graph of a function f(x) is y = 5x - 6. Evaluate f'(2). (a) 5 (b) 4 (c)…

A: We have given the equation of tangent line y=5x-6 of f(x) at point (2,4).

Q: Find the derivative of the function. y = In(3x²-x) + 4x

A: y=ln3x2-x+4xd dx(lnx)=1xd dx(xn)=nxn-1

Q: Consider the graph between two curves. Which of the following is the correct set up for the area of…

A: Consider the graph between two curves. To determine the set up of integral  that represents the area…

Q: 2. Find the derivatives of each of the following functions. You do not need to simplify your answer.…

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Q: Find all points (x, y) on the graph of y = x2 −6 with tangent lines passing through the point (3,…

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Q: Find the volume of the solid generated by revolving the shaded region about the x-axis. 6 X₁ = 1, X₂…

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Q: 19x² tan¹x dx = [

A: The given integral is 19x2tan-1x.

Q: 2 Functions f and g are defined by f(x)=2(3+1)₁³ ,x+0 and 1 g(x)==-=-3₁ X≠3 respectively. (a) Find f…

A: The given functions are:f(x)=23+1x ;    x≠0       and        g(x)=1x-3 ;     x≠3

Q: Consider the function ƒ(x) = −2x² + 8x – 3. f(x) has a critical point at x = A. Find the value of A:…

A: Application of Derivative

Q: 3, 3, 1 > and b Let a = . Find k so that a and b will be orthogonal (form a 90 degree angle). k=

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Q: Find a formula for the n" partial sum of the series 5- th The formula for the nth partial sum, s of…

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Q: 10. The average rate of change of f(x)= x² + x over the interval 0 ≤ x ≤ 4 is a. 20 b. 4 c. 5 d. 1

A: f(x)=x2+xinterval is  0≤x≤4formula for average rate of change is favg=f(b)-f(a)b-a

Q: TOPIC 4-5: L'Hôpital's Rule x²-25 x+∞5-4x-x² Q. #11 Please evaluate Lim a) Using L'Hôpital's Rule as…

A: L’hospital rule  limx— a f(x)/g(x)   = limx— a f’(x)/g’(x)   now find limit

Q: Find the inverse Laplace transform L¯¹{F(s)} of the given function. 8s² - 49s + 294 s(s² +49) Your…

A: given  Fs=8 s2 - 49 s + 294s  s2 + 49 and asked to find the inverse laplace transform of F( s ).

Q: Find the volume of a pyramid with height 28 and rectangular base with dimensions 5 and 7 using…

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Q: The average rate of change of f(x) = X a. 2 b. 0.5 over the interval 1 ≤ x ≤ 2 is c. -0.5 d. -1

A: we will find the required.

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: 2 Find the average height of the paraboloid z = x +y over the square 0 ≤x≤ 1,0 ≤ y ≤ 1

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Q: 4. Point of Diminishing Returns Assume that an advertising campaign is launched for a new product…

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Q: S Du Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate…

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Q: 3. a) Find the limit of the sequence an = (2n²+3)(n-1) n(n² + 1)

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: In this problem, p is in dollars and q is the number of units. (a) Find the elasticity of the demand…

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Q: Let f be the function given by f(x)=sin(2x)cos(1+x). What is the average value of fon the closed…

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Q: Evaluate the limit using L'Hospital's rule if necessary x 5 7 lim (1+1)

A: To find the limit

Q: Find the arc length of y = 2x³/2 on 1 ≤ x ≤ 3.

A: y=2x321≤x≤3arc length(L)=∫ab1+(dydx)2dxd dx(xn)=nxn-1

Q: Find the points on the cone ² = x² + y² that are closest to the point (5,2,0)

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Q: Suppose that f (x, y) = x³y². The directional derivative of f (x, y) in the directional (-3, 3) and…

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Q: The position of an object with respect to time is given by the following function: d(t) = d³ +21² -…

A: Given poistion function:- dt=d3+2t2-2

Q: K For the following demand function, find a. E, and b. the values of q (if any) at which total…

A: Given p = 700e-0.2q

Q: Find the derivative of the following function: f(x) = ³√x² -2 (a) f'(x) = 3 1/ (b) ƒ'(x) = 3³7x²…

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