find the area of the region bounded above by the curve y = 2e^-x + x, below by the curve y = e^x/2, on the left by x = 0, and on the right by x = 1

Q: 2. The seventh term of a geometric sequence is -2 and the tenth term is 128. Find the fifth term. 3....

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Q: Use the second derivative f"(x) = x(x+ 1)(x-3) to determine where the function f(x) is concave down....

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Q: Evaluate the integral cot 2x S- Vcot? 2x - 15

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Q: Use sigma notation to write the Taylor series about x = 4 for the function. 1 x + 3 1 -1* 7*+1 (x – ...

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Q: As x approaches 0, the left and right limits equal 3. However, the actual y-value at that point is -...

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Q: 3. (3 marks) Given that u(x, y) = f(y- a) +g(y +x) is a general solution to Uzz = Uyy, %3D for twice...

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Q: 1 Evaluate the integral I+2/3 dr.

A: We have to find value of given indefinite Integration.

Q: SV1+ vw_dw

A: ∫1+wdw  

Q: f (1,0) Based on the figure above, (f-1)'(0)

A: The figure given is   

Q: 8. Detemine the area of the region enclosed by the curve y = x +4 and y = x+4. %3D

A: The given curves y=x2+4 and y=x+4  

Q: I. Determine whether the series converges using any appropriate test. Identify the test for converge...

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Q: Determine the Laplace Transform of the functions shown and simplify.

A: Our Aim is to determine the Laplace Transform of the functions shown below:-14cosh (16t)+16sinh (16t...

Q: Evaluate the integral cot 2x S- Vcot2 2x – 15 V cot? 2x

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Q: p dq , for demand q and price p. Find the general equation q = f(p) where E = 3. (Hint: Set the elas...

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Q: Use the binomial series to find the Maclaurin series for the function. f(x) = V1+ x CO f(x) = 1 + -x...

A: From binomial theorem we know, 1+xn=1+nx+n(n-1)2!x2+n(n-1)(n-2)3!x3+....

Q: 6. Which of the following is not true about function? a. Function is composed of two quantities wher...

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Q: Find the nth Maclaurin polynomial for the function. 4x – 4 f(x) = n = 4 %3D X + 1 Pa(X) = || %3D

A: Here, the given function is: f(x)=4x-4x+1      =4x+4-8x+1      =4(x+1)x+1-8x+1      =4-81x+1

Q: Enter the value of L- 1.27].

A: Floor value of x  is given as the greatest integer that is less than or equal to x

Q: Let S be the plane defined by 5x-Sy+10z 0, and let T be the plane defined by 2x-2y+5z=-2. Find the v...

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c = 3 P (X) –

A: Taylor polynomial of 4th order of function fx at a is defined as: fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x...

Q: In (1 - 4x) = - In (1 - 4x) = ア- 4n O In (1 – 4x) = - 4n In (1 - 4x) = Identify the interval on whic...

A: To find the interval of convergence where the series is valid .

Q: dx 2V x3 - 3x x

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Q: Evaluate the integral V5+ 12x2 – 4xª xdx 2x2 – 3 (2x? - 3)/5+ 12x² – 4xª + 14Arcsin V14 +C {(2x2 - 3...

A: We will use substitution method to solve it.

Q: 11. The integral of an(In|4x=12 dx is bln|sec(ln(2x)ª)|. What is b? A. 2 В. С. 4 D. I

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Q: 8. dx du The integral reduces to k, where u = f(x) and for some ex + 1 constant k . Compute f(1). e ...

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Q: 20. Given: S 10 -dx Find: formula

A: Here we have to integrate the given function.

Q: 23. If u = f(x), then +2x² + 1 k + C for some constant k . x² + 1 Compute kf (1). (a) ¼ (b) – ½ (c) ...

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Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

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Q: dx du The integral , reduces to k=, where u = f(x) and for some ex + 1 constant k . Compute f (1). e...

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Q: 21. du Form Answer u 5sinx Ex. S V3+ 2cosx 3+ 2cosx -5V3 + 2cosx + C dx -2sinxdx Given: J – 3x 3 dx ...

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Q: EXERCIS Directions: Read each item carefully. Write sheet of paper. Evaluate the foillowing function...

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Q: One of the following is an improper integral. \. xV16 – In x ~In 3 dx dx In 2 V4 – ex xV16 – In x -I...

A: We have to find the value of improper integral.

Q: Find the radius of convergence and the interval of convergence. El-1)«(# + 2)2*+1 k2 + 4 A=1 Radius ...

A: Given series ∑k=1∞(-1)k(x+2)2k+1k2+4 want to find radius of convergence and interval of convergence 

Q: Evaluate the integral V4x4 – 12x2 +7 xdx

A: Using integration of square root of x2 - a2 and follow step 2nd . 

Q: Find dydx for y=ln2x3−x2

A: This question is based on derivative.

Q: From the definition of the derivative of f(x) as f (x+h)- f(x) f (x)=lim h→0 h derive a formula for ...

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Q: 2. Let dx be given . If u = e* + 1, then the resulting integral is F(u) du. Compute f(3). (a) 2/3 (b...

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Q: = 60 %3D = 30 %D =D3 %3D = ? %3D

A: From the given information,           3 × times of Red flower = 60                        

Q: Find the Maclaurin polynomials of orders n = 0,1,2,3, and 4, and then find the nth Maclaurin polynom...

A: Given function f(x)=eaxseries is given as p0(x)=f(0)p1(x)=f(0)+xf'(0)p2(x)=f(0)+xf'(0)+x22!f''(0)p3(...

Q: u du Form Answer Ex. S 3+ 2cosx 5sinx 5 -5V3+ 2cosx + C dx 3+ 2cosx -2sinxdx ī du 3 15. Given: S -dx...

A: This is a integration problem

Q: In3 ex i. dx In2 4- ex i. X/16 - Inx e 1 iI. i xInx In2 1 dx Ino.5 e2x + 1 iv.

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Q: -2r 2. Find de/dr of the function 0 = (cos(r))

A: Given problem:-

Q: Find the solution of the following initial value problem: an = 14a,-1 – 49a, 2; ao = 0, a1 = 6 %3D a...

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Q: dx The integral | can be rewritten as V1. - X (a) lim (-2+2v1 – s) (b) lim (-1+2v1 – s) S--00 S--00 ...

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Q: Determine the value of x of the continuous function: * х — 1 f(x) = {3x – 3 (-4x + 3 x 3

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Q: Express the following as a vector valued function 7 (t). 1. The line L defined by y+3=3x and z+1 =0 ...

A: We will express the line L defined by y+3=3x and z+1=0 hyperbola -x2-2x+2y2+4y=-2 as a vector valued...

Q: Evaluate the integral cot 2x /cot² 2x – 15 csc 2x +C 4 1 -Arcsec (B -Arcsec csc 2x +C 4 1 Arcsec 2/1...

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Q: d) Without expanding, calculate the marginal function for: TC = (2Q2 – 3Q + 7)5 %3D

A: Given

Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show ...

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Q: Solve the following differential equations. Indicate the (Differential Equations) method/s used at t...

A: (4x2+y2)dxdy = -xy ....(1)f(x,y) dxdy =ϕ(x,y)The given differential equation is ahomogenous equation...