Consider the initial value problem For what value(s) of y, will the solution of the ivp have a vertical asymptote at t = 4 and be defined in (-∞, 4)? Yo [y' = 3y² {y(0) = y₁ help (numbers)

Q: Convert the point (r, 0, z) = (2, 2π, -1) to Cartesian coordinates. Give answers either as…

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Q: Complete the following problems applying the Intermediate Value Theorem, when applicable. Complete…

A: (1) By applying the IVT to determine whether  has a solution in one of the intervals .(2) For . To…

Q: Evaluate the following one-sided limit. lim z+1 (z − 1)(z + 4) |z − 1| =Number

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Q: Evaluate the integral. (Use C for the constant of integration.) [(1 + √/sin(t)) cos³(t) dt

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Q: f(t) = 4t2;    t = 5, t = 5 + h (a) Determine the net change between the given values of the…

A: The function is f(t)=4t2 (a) The aim is to find the net change at t=5 to t=5+h

Q: The following chart shows student population in a certain elementary school over a 5 year period.…

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Q: For matrices X= xy Z W and O= O-X= (Simplify your answer.) 00 00 find the matrix O-X.

A: Consider the matrices

Q: 3. Suppose a stone is thrown vertically upward from a height of 96 ft above the ground in a vacuum…

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Q: d 4. Determine sin√x dx Space on next page in radical form]

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Q: Calculate the circumference of the following circle (a > 0). r = a cos 0

A: Calculate the circumference of the following circle (a>0).r=acos⁡θ

Q: ·Sex tan² (ex) dx 3 .fx cos ³ (x²) dx

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Q: The graph of a function is given. Determine the average rate of change of the function between the…

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Q: Evaluate the following limit. lim (ln(t) + In(6t + 5) — ln(6t² – 5t+3)) t→∞0 Number

A: Given data

Q: Let r(t) = (-5t³ – 1, t² + 5t³, 3t²). Find the line (L) tangent to (t) at the point (39, -36, 12)

A: r→(t)=⟨−5t3−1,t2+5t3,3t2⟩Find the line (L) tangent to r→(t) at the point (39,−36,12)

Q: Evaluate the integral. 2 + 1 dx

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Q: 1. Differentiate. a) y = 2cos (4x) b) y = 1+e²x e2x (Hint, consider creating an easier equation) c)…

A: As per our guidelines we can answer only 3 sub parts of the given problem so kindly repost the…

Q: Directions: Find the instantaneous rate of change. Make sure to show all your steps. 1) 3x3, at x=2…

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Q: Find the point on the graph of the function that is closest to the given point. f(x) = √√x, (7,0)…

A: To determine the points on the graph of the function that are closest to the given point.

Q: Cathy wants to determine the height of a Flag pole shown below. She uses a survey instruace to…

A: The figure

Q: Find the intercepts of the plane 2x+6y3z- 12 = 0

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Q: Find an equation in cylindrical coordinates for the rectangular equation x +ỷ =5y

A: Consider the rectangular equation

Q: The dimensions of a triangle are shown. cm 8 cm What is the area of the triangle? Use the number pad…

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Q: 5. A ball is thrown into the air and the vertical position is given by x (t) = -4.9t² + 25t + 5. Use…

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Q: Find each of the following for the piecewise function: f(x) = f(-4)= 3 x² + 3 -2x + 4 x 2 f(-5) =

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Q: 2. In Test 1, we have used the following theorem without a proof. Write up a proof for it. The…

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Q: Question 2.21) Find the interval(s) on which the following functions are continuous. Make sure your…

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Q: Evaluate the limit. AY lim x→3 x²2 +7x-√30 x-3

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Q: Consider the function x¹4 cos M Assume that we know that g(x) is continuous at x = : 0. (a) To…

A: Squeeze theorem:

Q: If g is the function defined by g (x) = 2cos²x-1 , then lim g (x) is equivalent to which of the…

A: given function to find Limit

Q: Consider the following. [² x (x² - 1)³ dx 0

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Q: find an inner and outer such that y=f(g(x)) then calculate dy/dx  y=tan5x^2

A: Given y = tan(5x²)

Q: Find the following using the table below. 1 23 4 1 13 3 3 X f(x) 2 4 f'(x) 14 4 2 g(x) 3 4 2 1 g'(x)…

A: given function

Q: If the population of an ant colony in  5  days is known to be  1100  and  P'(0)=3 , what is the…

A: For Linear Growth we have formula,

Q: I. Solve each system of equations using SUBSTITUTION METHOD {v=52 1. 5x - y = 6 2x²-3x + 2

A: To solve the following system of equations by using the substitution method.Note: Since the student…

Q: Write a polynomial function, in factored form, with real coefficient whose zeros and multiplicities…

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Q: Note: You must not use vector components to solve this question. You must use the Law of Sines and…

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Q: 8. Compute two fully factored derivatives and determine the exact coordinates of any points of…

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Q: 4 5 The graph of y = (x²-2)(x² +2) is shown to the right. Find the coordinates of the local maxima…

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Q: Evaluate the limit. lim x-5 x² + 3x - √40 x-5

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Q: If a is a vector such that ||a|| = 7, then what is a . a? √7 7 14 49 There's not enough information…

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Q: Find the equation of the circumference whose center is C(0, 0) and whose radius is equal to the…

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Q: d²w dz² w = 7z² e² Find d²w dz² for the given function. ...

A: Givenw = 7z²ez

Q: Analyze the function below. Which of the following is/are true? 8f()81818 x+2 as x→-1+, f (x) →∞ as…

A: Function is not defined where denominator is equal to 0.

Q: The current population of a certain bacteria is 5687 organisms. It is believed that bacteria's…

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Q: Find the parametric equations of the tangent line to the curve represented by the vector function…

A: In this question, we will find the parametric equations for the tangent line to the given curve.

Q: Differentiate the function f(x) (11x8-9x6+21x4+15x³-12x²+3) that f(x) = h (g(x)) For the toolbar,…

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Q: Sketch a graph of a function g that satisfies all of the following conditions: a. limh(x) = h(-2) =…

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Q: Write the equation of the vertical line at which the graph is discontinuous. Then, write what y…

A: f(x)=(x+5)(x+12)(x+7)

Q: 16. y' = (1 − y) cos x, y (π) = 2

A: To solve the following initial value problem.

Q: Find T, N, and K for the plane curve r(t) = (10t + 1) i + (6 −t¹0) j T(t) = 1⁹ √√1+118 (Type exact…

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