Find the average value gave of the function g on the given interval. g(t) = 2 1 + t²' [0, 9]

Q: Find the area enclosed by the ellipse a² b + y=-b√√√a²-x² y² 62 b y=1/√√a²-x² = 1 shown in the…

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Q: Use integration by parts twice to evaluate fet cos(3t)dt: Step 1: Let u = et and du + S fet…

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Q: A ball is shot out of a cannon at ground level. Its height H in feet after t sec is given by the…

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Q: 1. Given the following vector in 2D 100 m [E10°S], Determine the following: a. Another vector that…

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Q: can you explain how you got (x-2)=(t-3) and can you explain how you got the new limits because the…

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Q: Integrate by parts [2x(x-3)* dx Formula: Sudv=uv-fvdu,

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Q: (a) Use a calculator to find e0.7(rounded to five decimal places). eº.7% (b) Estimate eº.7 by using…

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Q: 1-16 Evaluate the line integral, where C is the given curve. 1. fcyds, C: x= t², y = 2t, 0≤ t ≤3

A: To evaluate the following line integral. ∫C y ds, C: x=t2, y=2t, 0≤t≤3 Note: Since, the student has…

Q: Use partial fractions to find the area of the given region. 7 16x² y = y 3

A: Now area of the region f(x) from a to b formula Area=int_a^b f(x) dx

Q: 10. Solve and check by integrating factor: {Integrating factor e[2(=)α = } y '+ 2 y = 4

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Q: x² √x² - 9 s dx

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Q: 25 lim x+c+ (x-c)³ 25 lim x+c¯(x-c)³

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Q: Suppose f(x, y) (a) ▼ f(x, y) = (b) ▼ f(-1.1, 6): = tan(x) + y and u is the unit vector in the…

A: f(x,y)=sqrt(tanx+y) , (x, y) = (-1.1,6) Unit vector in the direction <-1,1> Find the gradient…

Q: Use the Rectangular Approximation Method to approximate the area of f(x)=³ on the interval [0,8 with…

A: Using the Rectangular Approximation Method with 4 rectangles and taking the midpoint of the…

Q: Given that v = (0, -2) and w = (5, -8), what is w - v? A (5,6) B (5,-6) C (-5, -6) D (-5, 6)

A: Explanation of the answer is as follows

Q: Sketch an example of a nonconstant function f(x) such that ·Sª. f(x) dx = 8

A: ∫xndx=xn+1n+1+c

Q: 1. The function is given piecewise: ƒ(x) = cos(x) 0 X if x 0

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Q: Use power series to solve the differential equation (1+2x²)y"+6xy'+2y=0

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Q: Write the following numbers in Cartesian form (i.e., in the form a + bi). Use the principal value…

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Q: Use the Limit Comparison Test for 4n² + 2 n(n-1)(n-19) Σ' an bn n=25 to prove convergence or…

A: The given series: ∑n=25∞an=∑n=25∞4n2+2nn-1n-19We need to prove the convergence or divergence using…

Q: What is an antiderivative of the function x + 2xln(x)? x²ln(x)+2023 xln(x) +2023 In(x) + x xsin(x) +…

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Q: A house was valued at $120,000 in the year 1993. The value appreciated to $145,000 by the year 2001.…

A: We have, A house was valued at $120,000 in the year 1993. The value appreciated to $145,000 by the…

Q: Scot³ (x²) csc² (x²)x dx Туре u u |

A: To evaluate the following integral. ∫cot3x2 csc2x2 x dx

Q: Suppose that fx cos(x²)dx = G(x) + C = F(x). Determine the constant of integration C if F(0) = 2. 0…

A: Given Integral  ∫xcos( x2 )dx∫xcos( x2 )dx = G( x ) + C Given condition F( 0 ) = 2

Q: 4. The formula A = P(1 + i)" gives the amount, A, of an investment of P dollars after n years at 1%…

A: As per the problem the amount A of investment P after n years at i% interest compounded yearly is…

Q: X-25 (x-2) √√x²+2x Converges? Dieverges? dx AND WHY?

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Q: 4. Determine the vertex of the parabola y 2 2x + 15x using Calculus.

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Q: Find a plane containing the point (5,-2,8) and the line of intersection of the planes 7x+6y-z = 27…

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Q: 1. let y = x(x2+x)2  , Find y'   2. let f(x) = (5x)5 find f '(x)…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Write the name of the metric system prefix associated with each mathematical factor. Do not use any…

A: Write the name of the metric system prefix associated with each mathematical factor. Do not use any…

Q: What is the component form of resultant of 46 - 5ā? a = (1, -3) 6=(-1,2) Enter your answer by…

A: a=<1,-3>, b=<-1,2> Find 4b-5a

Q: 15. lim x-0 17. lim t->0 19. lim x-0 √1 + 2x 5¹ - 3¹ t et 1 2 x² X X √1 4x

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Q: x2 - 4 3 dx

A: The given integral is: I=∫x2-4x3dx

Q: Consider the graph of the function f given below. f(x) I -2 4 B) If h(x) 2 0 -2 2 x 4 A) If g(x) =…

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Q: Consider the following vector function. r(t) = ( 26, 12², 1²) (a) Find the unit tangent and unit…

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Q: Solve for the unknown quantities, if possible, in Exer- cises 5-16. 5. (1, 2) + (0, y) = (1, 3)

A: Note:- Since you asked multiple questions, according to our policy we can solve only first question…

Q: Solve the following differential equations dr² dy +7x16y=0, y(1)=3,y(1)=1

A: NOTE: Refresh your page if you can't see any equations. . The given DE is, compare this equation…

Q: What is the domain and range of the following function? 34. y

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Q: MATCHING LIST Match each pair of vectors with their dot product. v = 6i + 7j and w = -8i + 9j v=3i -…

A: (a) given v=6i+7j and w=-8i+9j

Q: Evaluate the integral. (Use C for the constant of integration.) √ 8 tan³(x) sec(x) dx

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Q: What is the value of c > 0 that maximises the function h = ln(c) — ct, where t is a positive…

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Q: What are the polar coordinates of the rectangular coordinates (-√3, 1)? (4, 11) (2, 11) (4, 5) (2,5)

A: NOTE: Refresh your page if you can't see any equations. . the given rectangular coordinate is, .…

Q: Use partial fractions to find the area of the given region. 12 x + 5x + 6 y -1 y 3 2 1 -1| 1 2 3 4 5…

A: The region is bounded by the curve y=12x2+5x+6 in the interval 0, 4. To find the area of the region…

Q: The expression √(3x - 2√x) equals Ax³/2. + Bx where A equals: and Bequals:

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Q: 19.) Find the indicated of 0. exact value of the trigonometric function CSC =-9/8, is in quad III 7…

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Q: The expression √√64x² equals næ” where n, the leading coefficient, is: and r, the exponent of a, is:

A: Given Expression 64x23

Q: Evaluate the integral. (Use C for the constant of integration.) [tan²(x) cos³(x) dx

A: let B=∫tan2xcos3xdx

Q: 20. Find the area of the region between the curve y sin x and y = cos x from 0 to π/2. a. 0.414 b.…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: F. dr. For example, the in Sc F. dr where =tb (1)'4- ((1)) 16.2 EXERCISES 1-16 Evaluate the line…

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Q: 3. Consider the following vectors: (2,3) & (-5,1) a. Find the dot product between them b. Find the…

A: We have to find the dot product and angle between two vectors.