Find the limit. lim (t i – 4j + t² k) (t i – 4 j + ° k) = j+ lim i+ k

Q: x2+8z-9 a+6 key values of the function were ADDED together, their SUM total would be: Given the…

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Q: Which formula is not equivalent to the other two? 10 (-1)*-7 -5 (- 1)* 3 (e) k-7 | 3 (2) k = -7 k+1…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivativ f(x) Vt3 + 2°dt f'(x) =…

A: Given query is to find the derivative.

Q: Evaluate the integral. 5 | 8x?dx xp. 1

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Q: If g(x) = 5 – x³, find g'(0) and use it to find an equation of the tangent line to the curve y = 5 –…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Express the Cartesian coordinates (-3, 1) as polar coordinates. (2, 330°) O (2V2, 150) O (2, 150)

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Q: Consider the function f(x) = 9(x – 2)²/3. For this function there are two important intervals: (-oo,…

A: The given function,      f(x)=9x-223

Q: A function f(x) and interval [a, b] are given. Check if the Mean Value Theorem can be applied to f…

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Q: Determine the type and stability of the critical points of the homogeneous systems: dx = x - 2y dt…

A: We have to determine the type and stability of the critical points of the homogeneous systems.

Q: 3. 2 What is the value of the integral 7xyz dxdydz ? 0, Select one: O 133/4 O 135/4 O 137/4 O 139/4…

A: To evaluate: ∫23∫12∫017xyz2dxdydz Let I = ∫23∫12∫017xyz2dxdydz First integrate with respect to x and…

Q: If cot (x) 23 (in Quadrant-I), find 30 sin(2æ)

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Q: Given that f(z, y) = z (2y+4) +y(7z - 14) is a potential function for F = (2y+4+7y, 2z + Ta - 14).…

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Q: A (x -3) dy X +y -.

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Q: Find all intercepts of the following function. 1 g(x)= - x-4 y-intercept: |0. x-intercept: and…

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Q: Convert the polar equation r2 = -2 sin 20 to a Cartesian equation. O +y? = 2 xy O12+)² = -4 xy…

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Q: Find the indefinite integral. (Use C for the constant of integration.) cosh(8x) dx

A: We have to find the indefinite integral ∫cosh8x dx.

Q: tanx sec*x dx. Use trigonometric groups.

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Q: Evaluate the integral. (Use C for the constant of integration.) (3× – 5*) dx -

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Q: 13 dx 12

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Q: An oral medication is absorbed into the bloodstream at the rate of  4e−0.04t  milligrams per…

A: Find the total amount of medication absorbed within the first 20 minutes

Q: Given f''(x) 25 sin(5x) and f'(0) = - 1 and f(0) = 2. | Find f() 6.

A: Given query is to solve the differential equation and find the valu of indicated function.

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Q: Find the approximate change in volume of a cube of side 'x' inches caused by increasing its sides by…

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Q: Estimate the area under the graph of f(x)= 3x between x 0 and x=1 using each finite approximation…

A: Note: As per our company guidelines we are supposed to answer the first three subparts of the…

Q: If these two y's, y1=e^tcos(t) and y2(t)=e^tsin(t) are both solutions to y''+j(t)y'+k(t)y=0, how do…

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Q: Suppose that f(x) = 3iV4x?² + 2 (A) Find all critical values of f. If there are no critical values,…

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

A: Given problem:- Find the critical number of given function h(p) =(p-5)/(p2+7)

Q: If f(x) tdt then f'(x) =

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Q: Question Using Rolle's theorem for the following function, find all valuesc in the given interval…

A: Given query is to find the value of c for the given interval.

Q: Evaluate the integral. 4 2х e dx 4 2x e dx = (Type an integer or decimal rounded to the nearest…

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Q: For the integral, tanx secx dx, if we let u = tan x, what is the re-written form of the integral:…

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Q: 8. Let y(x) be the solution of the differential equation ry-y-Ina such that y(1) 1. Find y(2). A…

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Q: 27. Jul 16,0 =

A: Given data÷ Vector u is given by u=ucosθi+usinθj Or  u=<ucosθ,usinθ>

Q: 1. Determine the type and stability of the critical points of the homogeneous systems: dx (a) = x –…

A: Solving

Q: 10 Convert the Cartesian equation 2 xy = 1 in polar equation form. r²cos2θ = 0 cosθsinθ = 1/2…

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Q: Evaluate the following limits x2+3x-10 lím 1. x+2 x2-8x+15 x-2 lim x+3 2-36 2. x-3 3. lim X+6 x+6…

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Q: f(x) Let lim = 2. Find limits below. f(x) + 6x (a) lim 2.x f(3x) (b) lim I+0 5x

A: Use the limit given above and simplify limit for a and b .

Q: 8. Let y(x) be the solution of the differential equation ry' - y = lnr such that y(1) = 1. Find y(2…

A: The standard form of the first-order linear differential equation is: dydx+Py=Q Where P & Q is…

Q: Convert the polar equation r- 3 cosa 5 sin A in Cartesian equation form. )x² + y² - 3x = 5y 1- 3x =…

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Q: Find f. f "'(x) = cos(x), f(0) = 8, f '(0) = 8, f(x) =

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Q: Find f. f '''(x) = cos(x), f(0) = 2, f '(0) = 6, f ''(0) = 3

A: Given, f'''(x)=cos(x) Taking integration on both side f''(x)=sin(x)+A…

Q: V5 +3 v3 - E-2 where k is an integer to be found. V5 + V3 Without using a calculator, show that Cs…

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Q: 3 if x 1 5 4 5 -1 -1 -5 -4 -3 -2 2 3 4 -2 -3 -4 -5 Clear All Draw: 2] 2.

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Q: 3x2+ 7x+28 A f (x) |*+ A x³+x²+7x Using Partial Fractions in evaluating dx, the decomposed fraction…

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Q: f(x) = In(4 x) domain vertical asymptote x-intercept (x, y) =

A: In this question, we will find the domain, vertical asymptote and x intercept of the given…

Q: b- Lim (3x³+x²-2/x²+x-2x³+1)

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Q: ng the shore and 60 meters from the sh mps into the water and swims from the second and swim at a…

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Q: a. Graph the function f(0) = 6 sin(0). 6- 4 -/2 3/2 -2 -4 -6 -8+ Clear All Draw: W b. Graph the…

A: We want to plot the graph.

Q: True or False, If f' (3) = f" (3) = 0. then I 3 MUST be an inflection point. (Remember = to give…

A: It is given that, f'(3)=f''(3)=0 then x = 3 must be an inflection point.

Q: dx = x – 2y + 1 dt dy = x + 3y – 9 dt

A: given