Find the limit. NOTE: Enter the answer using round brackets. t² + 8 1 = lim t+x6t²+7'2t (?, ?)

Q: Q1// Find the Area bounded by: x = -y? and x = y- 2

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Q: Which of the following is the Taylor series expansion of the function (x) =ex? with center at 0. 00…

A: Taylor Series representation of e-x about x=0 is given by, e-x=∑n=0∞-1nxnn!....(i)

Q: Find the area enclosed by the given curves a) y=x^3, y=-x, x=-1, x=1 b) y=x, y= -1/x, x=1/e, x=e

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Q: B) Find the number of bacteria after 5.5 hours.

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Q: Find each limit, if it exists. xA + 4 (a) lim x- 00 x4 - 3 (b) lim *+ 4 x- 00 x - 3 (c) x4 + 4 lim

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Q: dy 1. Find general solution for =x²y° +2y +x° +2. dx

A: Dear learner,  As per our guidelines we can provide the solution for first one only. Kindly post…

Q: f(x) = -x² + +9 square units

A: Given the query is to the area bounded by the curve.

Q: solve the following equation 2sin3x+sin2x+1=0, on the interval 0<x<2pi

A: 2sin(3x)+sin(2x)+1=0Let f(x)=2sin(3x)+sin(2x)+1 , 0&lt;x&lt;2πThe graph of f(x) is shown below:

Q: What is wrong with the equation? -5 15 dx = -4 64 -2 f(x) = x-5 is not continuous at x = -2, so FTC2…

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Q: Convert the rectangular equation to an equation in cylindrical coordinates and spherical…

A: We have to convert the given equation.

Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: ICLO-3 Use the graph to ist() de.x) dx and S(x) dx in order, from smallest to largest 05 0 0.5 52 25…

A: Here, the curve is above the x-axis for [0,1] and the curve is below the x-axis for [1,2] &amp;…

Q: Show that whether x5 + 10x3 + x + 1 is O(x4) or not?

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given problem:- Find the domain of r(t) and the value of r(t0)  r(t) = cos(πt)i - ln(t)j + √(t -…

Q: where t € [0, 1]. x = cost, y = sint-t,

A: Here we will find the equation of tangent and length of curve P,

Q: Find the derivative of the following function. (Do Not Simplify Your Answer After You Evaluate The…

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Q: In a circle of radius 25, find the length of the arc spanned by a central angle of radians. Round…

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Q: Graph the following function by using a convenient method. y = -3cos(30° - x/3)+ 7

A: This is a graph function

Q: Sketch the region bounded by the graph of the equations and find the area of the region. 1 y = , y =…

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Q: Use a parametri. tion to express the area of tne surface as a double Integrai. Then The portion of…

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Q: determine which statement is true

A: Follow the procedure given below.

Q: A-28. 3. |A| = 3, B = 8, and the angle formed by A and B is 45°. Determine A - 2B

A: We have to solve above question

Q: Use the properties to evaluate the integrals. 1. S; (1 + ) dx

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Q: Given the three vectors å ,b and ở in 3D. The following question is t termine if operation involving…

A: We can solve this as follows:

Q: Find dy/dx: solution in handwritten 1. y = , Vu du

A: Note:- Here limit of integral 0 to t4  then in your question we need to find dy/dt instead of dy/dx…

Q: 1+cosx Show that if f(x) = In| then f'(x) = -cscx. %3D 1-cosx

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Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

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Q: 44. Find f(x) if f(x) = 1/(2 - x).

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Q: 7. Evaluate (5 – x)dA where R {(x, y) : 0 < x < 5,0 < y < 3}

A: Double integral

Q: Find the general solution to the differential equation y''+5y'+6y=et

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Q: lim * 0 sin5x'

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Q: Find the n-th Taylor polynomials for 1 about x = 3 and express it in f(x) = x+ 2 sigma notation.

A: Taylor polynomial of nth degree of f(x) centered at 'a' :          f(x) = f(a)…

Q: Solve the differential equation 2xy + y²) dx + (x² + 2xy-y²) dy = 0

A: A homogeneous differential equation is one in which the degree of the function f(x,y) is the same as…

Q: Find the volume of a solid bounded by y=(x2 -4) and y=(2x - x2) about the axis y=-4.

A: formula : here

Q: Select the conic section represented by the equation. y 2 - x = 0 line parabola hyperbola circle…

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Q: Consider the polar equation defined by r = 5 cos(2 sin 6), where 0<0< 27. Determine the missing…

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Q: The graph of a function f is given. Use the graph to estimate the following. y 5 (a) All the local…

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Q: Solve the linear differential equation dy 2y x2 dx 1+x2 x2 y = x? tan-1(x) + c y 1+ x2 =1+x² +…

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Q: 9. A and B are unit vectors with an angle of 120° between them. Determine 3A +2B and it's direction.

A: We have to find the vector addition.   A→+B→=A→2+B→2+2A→B→cosθ

Q: Find the center of 8x 2 + 6y 2 - 32x + 24y + 8 = 0. (2, 2) (-2, 2) (2, -2)

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Q: Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate khefaltowing cartesian integrals by changing them inteequiv alent Palar integrals: dy dx

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Q: 6. The initial population of a town was 12000. After 5 years the population increased to 38000…

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Q: 8. If the graph of h(x) goes thro following statements are true fc

A: 8) y=h(x)g =h(x)This transformation only affects y-value.A(-16, 4)y(x=-16)=4, g(x=-16)=4 =2A' (-16,…

Q: Q1// Find the Area bounded by: x = -y2 and x = y - 2

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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

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Q: {In (n+10) – In (n+5)}°

A: an =ln(n+10)-ln(n+5)an =lnn+10n+5limn→∞ an =LIf the limit exists and finite, then the sequence is…

Q: Find the smallest value of x for which the series (x+ 124)" 2in(n) n 2 is conditionally convergent.…

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Q: Given two vectors u and v that form an angle of 60° (when joined tail to tail) and given that | V| =…

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Q: Integrate the following using partial fraction decomposition: integral sign  [(3x2+4x+56)  /…

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