Problem 4. Use the Substitution Rule to calculate each of the following integrals. You should show your work, in particular make it clear how your new variable is related to the original variable. (2) / 1/2 √/1-1 da dx x²

Q: Problem 3. The number of giant pandas in China at the beginning of the year 2000 was 9205. The…

A: The net change theorem says when a quantity changes the final value equals the initial value plus…

Q: Find the decomposition a = a + a₁ with respect to b if a = (3,4,2), b = (3, 4, 6). ab = (a||x, a|ly,…

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Q: K Find lim h-0 f(x+h)-f(x) h f(x) = -8x-7, x=2 The lim f(x+h)-f(x) h for the given function and…

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Q: In x 4. lim = 1 x2x-1 x f(x) 0.9 0.99 0.999 1.001 1.01 1.1

A: Note:- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Problem 5. Find I sin sin 2x dx

A: Our Aim is to evaluate the integral given below:-∫sin (2x) -(i) by using two methods :-(a) Using the…

Q: Find the derivative: Y = y' - 10 sin(x) + 3 5x9 - 2 =

A: The given function is y=-10sinx+35x9-2 We have to find the derivative of the function

Q: For the differential equation dy dx 5 + ex+y = 0, find its general solution.

A: The given differential equation is 5dydx+ex+y=0 We have to find the general solution of the…

Q: Write the linear equation for f(x), given f(1)=0 and the slope m=-2/3 A. f(x) = x 3 B. f(x) = −…

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Q: Given two vectors ū and v such that the length of u is 3 and the length of v is 5, and the angle…

A: As per your request , (3) Given that , u→=3 , v→=5 , θ=π3 Determine u→×v→2+2u→+v→·u→=?

Q: Find the solution of the given DE. 5. y' +6xy=0; y(n) = 5.

A: The given differential equation is; y'+6xy=o, y(pi)=5.

Q: ← Find the average value of the function f(x)=x²-23 on [0,9]. The average value of the function…

A: To find average value of the function.

Q: Let u = and v = Select all of the vectors that are linear combinations of {u, v}. (Check every…

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Q: Find the distance between (2, 1, -3), the given po (-6, 5,-4)

A: Topic:- geometry

Q: Use linear approximation to approximate ✓49.1 as follows. Let f(x)=√x. The equation of the tangent…

A: Tangent line equation of fx=x at x=49

Q: 2 1. (2xy-3x²) dx + (x ² + 2y) dy = 0

A: 2xy-3x2dx+x2+2ydy=0

Q: 8) Given two planes P₁:2x+4y+3z=4 and P₂:x-y-2z=-3 (a) Let L be the line of intersection of the two…

A: Given Planes :- P1: 2x+4y+3z=4 P2: x-y-2z=-3

Q: 5. For the constant numbers a and b, use the substitution = a cos² u + b sin² u, for 0 <u<, to show…

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Q: Calculate the 3 × 3 determinant. (Use symbolic notation and fractions where needed.) -2 6 -5 2 7 2 2…

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Q: For the given function f(x) and numbers L, c, and > 0, find an open interval about c on which the…

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Q: Evaluate the integral using an appropriate substitution. 10e +e -x 10e* e-x S C dx = +

A: sunstitute   10e^x-e^{-x}=u

Q: X Find the area of the surface generated by revolving the curve y = 18 The area of the surface is…

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Q: Find the equation of the least squares line. Ten students in a graduate program were randomly…

A: The equation of the regression line is y = 3.67 + 0.0313x  Therefore the option (B) is correct.

Q: Calculate the scalar triple product u (v x w), where u = (1,5, 0), v = (-8, -9,9), and w= = (4,…

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Q: Find the G.S. (y2-2xy + 6x) dx - (x2 - 2xy +2) dy=0

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Q: (x+ d

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Q: 2. Find the Inverse Laplace Transform of the following: b. L-¹{2+15+13)

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Q: Find the solution of the given DE. 6. y'+²y=-x³y³; y(-1)=2 .

A: y' +2xy=-x9y5

Q: #1 Cπ/2 ST 0 (8 + 4 cos x) dx

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Calculate the cross product assuming u xw = (8,6, -2) (Use symbolic notation or fractions where…

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Q: A certain bacteria culture is known to grown at a rate proportional to the number of bacteria…

A: let   p=amount of bacteria present   thendpdt=growth rate

Q: -3x Let G(x)=x2-9 A. Factor the denominator. B. State the domain of G(x). C. Determine the…

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Q: 3. Find the derivative of each function. Use proper notation, and simplify your answers. Thi…

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Q: 2. The height of a golf ball after t seconds is given by s(t) = 24t - 4.9t² meters. (a) Find the…

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Q: a. Use implicit differentiation to find the derivative p. Find the slope of the curve at the given…

A: Given

Q: Solve the right triangle. 450 3m Find the length of the side opposite to the given angle. (Round…

A: Given query is to complete the triangle.

Q: 28. (xy² + x − 2y + 3) dx + x²y dy = 2(x + y) dy; when x = 1, y = 1. - ANS. (xy - 2)² + (x + 3)² =…

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Q: 12x2 +2 (+x)dx

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Q: (e) Find equations of the horizontal and vertical asymptotes of the graph of f(x). HA VA:

A: Given query is to find vertical and horizontal asymptotes.

Q: 9. Eric wants to make a cylindrical water tank from sheet-metal. It must have a top and bottom. The…

A: Volume of the cylinder , V =πr2h ; where , 'h' is the height and 'r' is the radius of the circle.…

Q: Suppose that a function f(x) is defined for all real values of x except at x = c. Can anything be…

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Q: Assume that u. v = 6, ||u|| = 8, and ||v|| = 5. Calculate the value of (9u + v) · (u — 3v). (Give…

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Q: Question 9 Find the slope of the line that is tangent to the graph of f(x) (E) None of the choices 2…

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Q: II. Find the equation of the normal line to the curves at the point of tangency, if given. 1. y…

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Q: Use the method of Lagrange multipliers to find the maximum and minimum values of the function…

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Q: Calculate v x w = (u1, U2, U3). v = (7,5,2) w = (-6, 6,-5) (Give your answer using component form or…

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Q: Find the inverse Laplace transforms of the following: 7 S-4 (a) Ans: 5 3 + 1 16 + 7 641 144

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Q: 10. The national debt of a South American country t years from now is predicted to be D(t): 65 +9t3…

A: Topic- Application of derivatives We are given, Predicted nationl debt of a South American country t…

Q: he graphs of y = f(x) (solid) and y = g(x) (dashed) are shown. The two graphs intersect at ( Region…

A: Topic:- application of integration

Q: 1. Evaluate lim h→0 if f(a+h)-f(a) h ƒ(a) = a² − 4a +6 O4a-2 O2(a+2) O None of the Choices O2(2a-1)…

A: Given function:- fa=a2-4a+6

Q: Calculate the third derivative of y(x) = (4x² + 2) (5x³+3) (Use symbolic notation and fractions…

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