For the constant numbers a and b, use the substitution z = a cos² u + b sin² u, for 0

Q: Use Gaussian elimination and Gauss Jordan method to solve the system of linear equation. x - 2y-6z =…

A: The given system of linear equations, x-2y-6z=122x+4y+12z=-17x-4y-12z=22 We have to find the…

Q: 3. Check for homogeneity and obtain the general solution. (Let 4C=C) (x² + y²)dx + xy dy = 0

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Q: Find the integrals: 1- xdx A. -2/3 (1-x)3/2 B. 2/3 (1-x)3/2 + C C. -2/3 (1-x)3/2 + C D. -2/3…

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Q: Solve the triangle. Round the answers to the nearest integer. y= b= C= IN M. 0 in in 75% 15 in Y b…

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Q: y(x) = C₁ e ² + C₂ e ²*, + 4 SiN X, Y (0) = 1, y' (0) = -1

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Q: Find dy dt || dy dt for y = sin 2 (3nt – 4).

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Q: Use the tabular method and the properties of limit to find the limit X 1 1) lim 2 3 X-0 ()

A: limx→02{13)x =2 since,  limit f(x)= L exists. By Tabular method property  -- limit f(x) exist and is…

Q: Find the general solution of each of the following. rdp-(p+√pr)dr=0

A: Our Aim is to find the general solution of the following given below:-rdp-p+prdr=0 -(i)

Q: 3 Calculator active. Line L is tangent to the graph of y = 2 sin x at the point (k, 2 sin k), where…

A: Equation of tangent line L of a curve y=f(x)  at a point (a,b) is given byy-f(b)=f'(a)(x-a)

Q: 3x Solve for the complete solution of the differential equation: y" — 6y' + 9y = e³x Inx. What is…

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Q: Q2: Use the substitution x² = sing to show that 1 √ √ ² x dx = [] 4√2TE

A: See this solution in below.

Q: 3. The linear equation f(x) = x is called the identity function. (a) What is the derivative (slope)…

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Q: 86. f(x) = √x, g(x) = 2 x - 4

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Q: Find the derivative of the function using the definition of derivative. F'(v) = F(v) = V V + 3 3…

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Q: Prove that lim x-√3 1 1 3 C For a function f(x) that is defined in an open interval about c, except…

A: Solution is here

Q: Then (fofof)(x) = || (gogog)(x) = ((fog) - (gof))(x) = ((f+g) o (f-g))(x) = f(x)=2x-1 and g(x) = 3x…

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Q: then m = (q²b²³) 1/10 9-1/261/5 = and n = qmbn 1/10

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Q: Suppose that f is continuous on [0, 6] and that the only solutions of the equation f(x) = 3 are x =…

A: f is continuous on [0,6] and that the only solution of the equation f(x)=3 are x=1 and x=5.If f(4)=5…

Q: (e) Finally, consider f along rays emanating from the origin. Note that these are given by y = mx,…

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Q: What volume of refrigerant should be recovered for disposal from an oldrefrigerator? The length of…

A: Consider a cylindrical pipe with diameter 14 inch and 15 feet of long. To calculate its volume.

Q: Use the method of Lagrange multipliers to solve this exercise. Hercules Films is also deciding on…

A: The given demand equation is  q=198000-11000p The revenue function is Rp,q=q·p. As the cost per copy…

Q: The equation y +y-xy = x' defines a curve in the xy-plane called an elliptic curve. (a) Find the…

A: Given equation is is y2+y-xy=x3   .....1

Q: A quadratic function f is given. f(x) = 8x² - 16x + 1 (a) Express fin standard form. f(x) =

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Q: Consider the graph below of the function g(x) to evaluate the integrals The graph consists of two…

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Q: Solve the given differential equation (2x + 4y - 1) dx (x +2y-3) dy = 0 Ox-3y-In (x+2y-3) = C O 2…

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Q: Use the IVT (intermediate value theorem) to show that the given polynomial f(v)= 2v2 + 3 - 3v has a…

A: Here we have to use the intermediate value theorem.

Q: (x + 2y — 2) dx + (2x + y + 5) dy = ○ (x + 4)² − 2 (x + 4) (y − 3) + 4(y − 3)² = C O (x+4)² + 2(x +…

A: We have to find the solution of the given differential equation.

Q: 1. Circle the function if it is a (a) f(x) = 3x³ - 2x² + x (b) f(x) = 5x ² +5x² (c) f(x) = 2…

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Q: For the function f(x, y) below, determine whether there is a value for c making the function…

A: The transition value is x = 4   The function f is continuous at all points (x,y) where x is not…

Q: 1. f(x). = X+I

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Q: Find the standard form of the equation of a parabola opening to the right such that the endpoints of…

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Q: Find an equation for the line tangent to the curve y = (√x + 8)(x4 + 3) at x = 1. y =

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Q: Find the area of the sector of a circle with radius 17 miles formed by a central angle of 55°: what…

A: To find the area in square miles of the sector of a circle with radius 17 miles formed by a central…

Q: 3. A flag is raised vertically from a pole at a constant rate of 0.5 m/s. A point B on the ground is…

A: see below the answer and calculation

Q: Consider the graph below of the function g(x) to evaluate the integrals. The graph consists of two…

A: The integral is consist of area under two straight line and one semi circle

Q: (a) Show that y = e(c₁ cosa + c₂ sin x) is a general solution of y" + 2y' + 2y = 0. (b) Deter- mine…

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Q: 4.3 Stretching (a) Let f(x) = r². How do the values of f(0) and 2f (0) differ? (b) Let f(x) = 1².…

A: Solution

Q: Find the following limits: 1 1 5+x 5 x a. lim: x-0 b. x²+1 lim x-1- |x-1| C. -2x lim x +∞ √9x²-3

A: See this solution in below.

Q: a b= Note: Triangle may not be drawn to scale. Suppose a = 2 and A = 50 degrees. Find: C= B B = b…

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Q: The graph of the function f(x) is shown below. f(x) f(-1) is f(0) (a) Using the figure, find the…

A: Here we have to use the concept of derivatives

Q: In Exercises 5-14, determine the convergence of the given series using the Ratio Test. If the Ratio…

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Q: 1. A carpenter can construct book cases at a cost of P400 each. If the carpenter sells the book…

A: Given:- Carpenter sells the book cases for x pesos each And 300-2x book cases will be sold per month…

Q: Determine if the improper integral converges or diverges. 6- sin p 62 converges Odiverges do

A: We need to choose correct option.

Q: Check whether each differential equation has the indicated solution. Determine which solutions are…

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Q: Determine the Laplace transform of the function f(t) = t^2.  ( t squared

A: We have to find the Laplace transform of t2.

Q: What is the integral of x(x + 2) dx? A. x³/3 + x2 + C B. x³/3 + x²/2 C. (x+2)/2 D. x³/3 + x²/2 + C

A: We know, ∫xndx= x(n+1)/(n+1) , for any real number n

Q: Y = Ax² + Bc -X

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Q: dI (a) dy = -2xy, (b) xy' + 3y = 0; y(1) = 2, (o) +27= 10; 7(0) = 0, dx

A: According to guideline I can answer maximum three subparts.

Q: 3) Use the appropriate integral formula for the length of a curve represented by a function y = f(x)…

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Q: Find fogo h. Chec fogoh = f(x) = 9x - 2 g(x) = sin x h(x) = x²

A: Since you have asked multiple question, we will solve the first question for you as per our guide…