Find the area under the graph of the function y=2-x-x² over the interval [-2,1].

Q: Evaluate the definite integral. 18t (elst i+e¹j+t k)dt S (¹²¹ ₁+ (e-1) i-(¹-1) j+k els 1 - (e¯¹ − 1)…

A: Follow next step

Q: 5. The velocity function of a moving particle on a coordinate line is v (t) = t³ + 6t² + 11t + 6.…

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: 5x-10 Find the area under the curve of f(x)=- 05 O-10In 2 O 5-10lm 2 0-5 from 1 to 2.

A: Solve the given

Q: The temperature in degrees Celsius (C) in Toronto starting on March 1** can be represented by the…

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Q: Find the area that the curve encloses and then sketch it. r = 11(1 + cos ?)

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Q: determine maximum/mininum local values and its saddle points for this function  f(x,y) = 3x^4 +…

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Q: Solve the given differential equation by undetermined coefficients. y'' + y = 6x sin(x)   y(x)=

A: Follow step 2nd .

Q: Find the arc length L of the graph of r(t). r(t) = 1³ i + 1 j + = √61² k, 3≤1≤7

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Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 1 4x - 7 dy

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

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Q: 5. Does the function f(x) = e2x - 2x have any points of inflection? Justify your answer.

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Q: 5. Evaluate sin y - dy dx y

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Q: (x+1) dx 13 (メ-

A: We have to solve above question

Q: Find the nth derivative of y = In(16x2 – 9).

A: Given y=ln(16x2-9)

Q: c) Period d) f(990°)

A: Follow the procedure given below.

Q: n k=1 Note: Your answer should be in terms of n.

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Q: Find the x-value maximizing the shaded area on the interval 0 < x < 18. One vertex is on the graph…

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Q: Find an equation of the line tangent to the curve r = sin 30 at the point where 0 =

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Q: 2 Evaluate thefallowing cartesian integrats by - changing theminteequivalent Palar integralse 4- to…

A: Solving

Q: thu2 Evaluate khe faltowing cartesian integratby - changing them inte equivalent Polar integrals 2.…

A:

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: determine which statement is true

A: Follow the procedure given below.

Q: Find two positive numbers satisfying the given requirements. The product is 172 and the sum is a…

A: We find two positive number that product is 172 and sum is minimum.     Here i attached the solution…

Q: Match the function with one of the graphs below using horizontal asymptotes as an aid. Am 0.5 0.5

A: This question is based on graphing a function using horizontal asymptote.

Q: Numerical solution of Ordinary differential equations Consider the following initial value problem…

A: This is a problem of numerical method . Based on modified Euler method we will answer the question.

Q: Evaluate the following integrals by substitution. Show your complete solution. Express your answer…

A: We have to find integral solution

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

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Q: x²+x dx (x²+1)(x+2)

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Q: A student is asked to determine the polar coordinates (r, 8) corresponding to the Cartesian…

A: Let's find.

Q: Use Newton's method to approximate a root of the equation z + c + 3 - 0 as follows. Let I, = -1 be…

A: Let's find.

Q: Find the area of the region enclosed by the inner loop of the curve. r = 2 + 4 sin ?

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Q: a²z Determine a²z if z = tan- r - r r2+92°

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Q: A MANUFACTURER NEEDS TO MAKE A CYLINDRICAL CAN THAT WILL HOLD 1.5LITRES OF LIQUID. Determine the…

A: Follow the procedure given below.

Q: ield F = (A, B, C) such that A = 2zx, B = 3z + 2y, 0,0,0) = 1 and C is independent of

A: We have to find the following conditions according to the given information

Q: Find the Laplace transform of sint 0<t<27 f() =

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Q: If A =27+7-, B =-T+27-4k, and A +B +C =27+7+ 2k, what is C? 7.

A:

Q: Find the area (in square units) of the region under the graph of the function f on the interval [0,…

A: Given fx=10 ex on the interval 0,3 The formula to calculate the area under the graph y=g(x) on the…

Q: 3. An airplane with an airspeed of 80 meters per second is due east, gaining altitude, and has a…

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Q: Find the exact length of the curve. y2 = 64(x + 1)3,   0 ≤ x ≤ 1,  y > 0

A: Given,             y2=64x+13 , 0≤x≤1 , y&gt;0To find : Find the exact length of the curve.

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

A: Given    differentiate

Q: 2.Figure out the following = 2t2 +Int, t>0 dy. = cos(t – 1) c.f(z) =| -1|,9(z) =| 1.f'(1)?g/(0)? ?…

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Q: Show the repeating decimal .2727272727 repeating.... as an infinite geometric series. Give sum of…

A: This question can be solved using the concept of infinite geometric series.

Q: Find dy/dx: rsinx 1. у %3D Sm* 3t2 dt

A: I am attaching image so that you understand each and every step.

Q: Solve the given differential equation by undetermined coefficients. y'' + 5y = −180x2e5x y(x)=

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 3 1 = lim t+oo 8t² +9' 5t, (?, ?)

A:

Q: Let the graph below represent f(x). For which values of x is f(x) increasing? 20 16- 12- -5-3-2 8+…

A: The graph of the function f'x is To evaluate: The values of x for which fx is increasing.

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

Q: WHAT IS -1- ?

A:

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: 9-x2 dx x2 Evaluate:

A: