1. Evaluate: 00 e3z . Te + e5rjz dz

Q: Use the Lagrange multipliers method to find the maximum and minimum values of the function f(x,y) = ...

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Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x2 − x − ln(x)   inter...

A: f(x)=x2-x-ln(x)f'(x)=2x-1-1xf'(x)=02x-1-1x=02x2-x-1x=0(undefined at x=0)2x2-x-1=0(2x+1)(x-1)=0critic...

Q: Use your khowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z = e...

A: Here we are using simple differentiation method. First find out the first derivative of z then the s...

Q: Find the vector component of v = (4, – 1, 7) along b = (4, 8, –8) and the vector component of v orth...

A: The vector component of v along b is r=v·bb2 b The vector component of v orthogonal to b is u=b-r

Q: Use the Root Test to determine if the series (-1)" 2/n en? (2n² – 1)" - n=1 converges or diverges.

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Q: the sum. Use a model 1 1 3 3 1/3

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Q: Compute ∆y and dy for y = x^2 − 4x when changes from x = 3 to x = 3.5.

A: Topic:- application of derivatives

Q: Question 14 Evaluate and simplify the integral x +æ+3 a4+6x2+9 Show your solution. Upload Choose a F...

A: A detailed solution is given below

Q: Solve the following differential equations of Linear Differential dy Equation y– 2x . dx =x(x+1)y

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Q: Find  v  if  r = 3  inches and the point rotates at  15  rpm.

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Q: Determine if the series is absolutely convergent, conditionally convergent, or divergent. 2n + 1 (b)...

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Q: Using Laplace Transform, solve y" + 2ty' – y = t when y(0) = 0, and y'(0) = 1. %3D

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Q: Determine the area bounded by the curve y=9x/5 and the line y=x-2 A. 3.43 sq. units B. 6.86 sq. unit...

A: Let's find. 

Q: Use the Endpaper Integral Table to evaluate the given integral. If you have a CAS, use it to evaluat...

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Q: Let an​ be an arithmetic progression, for which a1​=15 and d=3. Find the sum of the first 10 element...

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Q: 2. Fill in the blanks Let y be a solution of the differential equation y' = , where – 1 < x < 1, –1<...

A: ∫1a2-x2 dx = 12aln1+x1-x+C

Q: Find dy/dx of the following function using Chain Rule. y=(-3x5 +1)3

A: we use chain rule for differentiation y=(-3x5 +1)3 dy/dx =3(-3x5 +1)2(-15x4) dy/dx = -45x4(-3x5 +1)2...

Q: Determine the area bounded by the curves y² = 4x and y² = 8(х — 1). A. 1.56 sq. units B. 3.12 sq. un...

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Q: Solve the equation y' + y · tan (x) = sec(x) Ans y sec(x) = tan(x)+c %3D

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Q: Finding the Area of a Region In Exercises 15-30, sketch the region bounded by the graphs of the equa...

A: Let's find. 

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

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Q: Find the area of the triangle with vertices P(1,6, –6), Q(0,0,0) and R(3, 4, 1). NOTE: Enter the exa...

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Q: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph illust...

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Q: 1) Use the definition of the partial derivative to find af given, əx f (x, y) = x²y + 2x + y³ %3D 2)...

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

Q: Prove Vr, y E Z, if ry is even and y is odd, then r+y is odd.

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Q: 1. Using Logarithmic Differentiation, find given that dr -3 sec-(VT) y = 4"(log21)«ch z'

A: To find derivative using logarithmic differentiation  keep this formulas in mind  log ab= b log a lo...

Q: dy Show that the analytical solution for this problem = 4 e081 - 0.5 y) dt (e0.81 - el-0.5 t) +2 e-0...

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Q: If L is a line in 2-space or 3-space that passes through the points A B, then the distance from a po...

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Q: e diagonals of the parallelogram nt sides.

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Q: Consider the hyperbola of equation: (x – h)² (y – k)2 a2 62 whose foci are (-3, 2) and (9, 2), and t...

A: First find distance between foci Then use formula

Q: For the given functions, find the domain, range and sketch the graph: 1. y = (2 + 3x)/(x – 1) ------...

A: We have to find domain,range and graph

Q: S sine sin (cose) de A. cos (cose) –cos³(cose) -cos B. cos (cose) + cos (cose) +cos (cose) + C C. co...

A: Solving the problem by finding the derivative.

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 20j as ...

A: By using vectors we have to find the lengths of the diagonals of the parallelogram that has i+j and ...

Q: Find the sum by adding each term together. Use the summation capabilities of a graphing utility to v...

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Q: P(x) = 8x + 26x - 67x + 15; a = -5, b = 2 = -5: -5 8 26 -67 15 e the row containing the quotient and...

A: Topic:- polynomial

Q: : Solve-Using D-operator dy dx + Зу - 5х — е t - 0 dt %3D dt dx dy +x + y-3 = 0 dt %3D dt

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Q: Express the following radian measure to degrees. 1) 150 2) 210 3) 100 4) 120

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Q: Use a calculator or program to compute the first 10 iterations of Newton's method for the given func...

A: Converges after 4th iteration 

Q: Make the indicated u-substitution, and then use the Table of Integrals to evaluate the integral. e6x...

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Q: phs of the equations, (b) analytically, and (c) us of the graphing utility to v

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Q: What is the common ratio of the geometric progression 3, -6, 12, -24, 48...?

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Q: 9. Sketch the solid obtained by rotating the region underneath the graph of the function f(x) = Vx2 ...

A: The answer is in step 2.

Q: Let f : R R with f(x) = -2x +5 Prove that f is onto.

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list.) h(x) = si...

A: To find the critical numbers of the given function.hx=sin2 x+cos x, 0&lt;x&lt;2π  

Q: Find the area of the triangle with vertices P(1, 6, –6), Q(0,0,0) and R(3, 4, 1). NOTE: Enter the ex...

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Q: Let an​ be an arithmetic progression, for which a3​=13 and a11​=25. Find a7​

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Q: S 3x° V1 – 2x3 x3 – 3x if a 0 1. Let f(x) = Evaluate S, f(x)dx

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Q: Use a calculator or program to compute the first 10 iterations of Newton's method when they are appl...

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Q: 3. Find the area of the region bounded by x = 3 – y and the line y = x - 1. Sketch the graph of the ...

A: Given: x=3-y2 &amp; y=x-1   Now find the point of intersection between the given curve and line. y=3...