Find the limit. NOTE: Enter the answer using round brackets. t² +3 1 = lim t+ (?, ?) 8t2 +9'2t

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 6x²y²j

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Q: Find the area bounded by r = 6cos (30).

A: Given: r=6cos3θ

Q: Use AXYZ, as needed, to complete the given parts. Part 1: Z 15 cm Part 2: Part 3: Part 4: Y 7 cm X h…

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Q: 10. Consider the region bounded by the graphs of y = tan-¹x, y = 0, and x = 1. Find the area of the…

A: Let's find.

Q: Find the curvature of the curve. r(t) =<2t, - 3sin t, 3cost)

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Q: Activity 2: Solve each function below the letters and decode the unknown word in each number. Once…

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Q: Find the instantaneous rate of change cope of the tangent line to 2 (3,-2) 1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2. Evaluate each of the following limits using the function f(x), defined below. If the limit does…

A: The given function is: f(x)=x+3x2+5x+6

Q: 4. Find the antiderivative of 1-t4 = CS the t that satisfies the given condition R(1) = 4

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Q: The first derivative of the function f(x) is given by its graph.. f'(x) 3- 2-

A: A.  Function is increasing when f'(x) &gt; 0  from graph  Function is increasing…

Q: Find curl(F x G) = V x (F x G). F(x, y, z) = i +5xj + 3yk G(x, y, z) = xi - yj + zk

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Q: Let C₁ be the circle r = 3 cos 0 and C₂ the cardioid r = 1 + cos 0. O (a) Find all point (s) of…

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Q: 8. teyty dy

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Q: This is the length of the major axis, not the minor axis.

A: Apologies for the inconvenience.   Given equation is: 7x2+y2=49 We write it in the form: x2a2+y2b2=1…

Q: Sketch a function that is continuous on (-∞0,00) and has the following properties. Use a number line…

A: We need to choose correct options for graph of f'(x).

Q: find dy/dx of each equation using implicit differentiation. a. (x+y) / (x-y) = y2 b. 2xy - y2 = 3

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Q: Determine whether the improper integral diverges or converges. S™× x²e-x dx converges diverges…

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Q: lim- LIMIT VALUE: z²-16

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question..…

Q: The fadius of a right Circular cylinder is increasing at a rate of 2 units Per Second. The height of…

A: Rate

Q: Consider the function f that is continuous on the interval [-5, 5] and for which 5 f(x)dx = 4.…

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Q: Consider a triangle ABC like the one below. Suppose that A= 116°, C=36°, and a = 19. (The figure is…

A: A triangle ABC has A=116°, C=36°, and a=19

Q: he equation of the line that passes through the point (-4,-2) and is parallel to the line y=4x-8 is…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. | ||ti + 1²3|| dt =

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Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m - n)] dx A…

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Q: h(x) = f(gx)) calculate the following derivatives using the table a) h'(3) b) h'(2)

A: Given

Q: Problem 1: Obtain ODE by eliminating arbitrary constant A, B, and C y = Ae2x + Be + C

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Q: - у = 3x-2 4x-5

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Q: For the following: a) Determine the intersection points. b) Draw a sketch of the graph. c) Find the…

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Q: Calculate the work expended when a particle is moved from 0 = (0,0) to Q = (4,4) along the segments…

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Q: Evaluate the iterated integral. [[ (x + y) dx dy

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Q: Consider the curve C with parametric equations given below, defined for t ∈ R. (a) Determine the…

A: We use the properties of parametric curve

Q: (-5,5) 14(x)=x²-19 9. f(-5) = (5)²-19 = 25 -19 - 6 b. lim x²-19 X→-5 = (-5) ² -19 = 25-19 C f(-5) =…

A: Let's find.

Q: The f e²x +e-2x e2x-e-2x dx is -2x1 {A}={In 2x te e e2x-e-2x + C 2x {B} In|e²x −e-²x | + C {C} -2…

A: To solve the given integral using substitution.

Q: Part 2: Exponential Growth and Decay and Logistic Growth Model (3) Suppose an experiment was…

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Q: 3. Find the derivative y' for each of the following curves/functions. Show all work toward your 12…

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Q: 2 S(²/33 -3 + 5x² + 3) dx

A: Given,            ∫2x3+5x2+3dx

Q: At the end of each month, for 24 months, $200 is put into an account paying 9% annual interest…

A: Solution of given question is written in below steps.

Q: Find the laplace transform of ƒ (t) = 6t³ + 4t² – 3 OF (s) -3s³ +8s+36 84 OF (s) 36s³ +88-3 84 OF…

A: A detailed solution is given below.

Q: Find the 6th term in the binomial expansion below with Sigma notation. 8 3 3 / 4.x²³ - √x. - 3)

A: Let's find.

Q: 4 3 2 +..

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Q: limn o 9-h-3 h 1 6

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Q: If ả = 2ỉ + 33, b = j – ỉ and ở = 33 are vectors in 2D, then determine the of a + 3b + c

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Q: Convert the following lines to parametric equation. a) l₁: = (1,0,1) + t(1,0,−2), t = R Z-3 b) 1₂: x…

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Q: dy √e²y-1 S

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Q: A company can buy a machine that is expected to increase the company's net income by $15,000 each…

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Q: Determine whether the sequence a₁ = find the limit. Show All Your Work! 1+9n² 1+n² converges or…

A: Given  find limit

Q: 2 The √tan x secxdx is {A} tan³/2x-tan7/2x + C {B} tan³/2x + ² tan7/2x + C {C} tan5/²x + tan7/²x + C…

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Q: the following 2 √x² √₁ + x dx aluate

A: Given query is to find the integral.

Q: [10 sin(2x) cos(2x) √ cos²(2x)-5 dx O a. 5 (cos² (2x)-5) ³/5 + C 3 5 O b. -(cos² (2x)-5)³/2 + C OC.…

A: To evaluate the given integral.

Q: dy e2y-1

A: