1. The sum of two positive numbers is 10. Find these numbers if the sum of their squares is a minimum.

Q: 3. Compute the scalar line integral 3 y – xz ds where C is the line seg- ment from (0, 1, 1) to…

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Q: th Use the ri"-term test to find wether the fottowing Sexies exe divergent or not- n+2

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Q: F(x, y, z) = (2xe*) i+ (2y + 3y?22)j+ (x²e* + 2y³z) k is conservative. Find a functionf such that F…

A: To find the function f  And then evaluate the line integral along the given curve.

Q: If hyperbola 36x^2 - 49y^2 - 100 = 0 has an eccentricity of e= √85/7, what are the asymptotes and…

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Q: Given the function f(x)%3D 2x2 f(x + h) - f(x) Find the difference quotient h f(r + h) – f(x) Find…

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Q: 3 6 Evakuate the determinant for the followeng matrix 5/ 1 OAR OC.

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Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile…

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Q: Given that s(x)=(−1)/ (x+8) +(9)/(x−4), what is the antiderivative of s(x)? (Do not include the…

A: sx=-1x+8+9x-4

Q: 3. a) Use the sum of the first 10 terms to estimate the sum of the given series. n-1 b) Improve this…

A: We have to find the sum and improve the estimates.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Suppose that f is a function given as f(x) = 5x 1. Simplify the expression f(x + h). f(r + h) = f(x…

A: Given query is to find the derivative of the expression.

Q: Determine whether the following equation represents an exponential growth or exponential decay.…

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Q: Consider the following. u = (5, 7), v = (4, 2) (a) Find the projection of u onto v. (b) Find the…

A: Given u=5,7, v=4,2

Q: (x² – 9) + xy = 0 dx

A: We have to solve the differential equation x2-9 dydx + xy = 0

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 3t, y =…

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Q: D. Find the area of the region bounded by the given curves. Breaking 1 NEWS x2 = 4y 3 y? = 4x %3D 2.

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Q: - 5 2x +1 Calculate the derivative function of g(x) Write your result as a single fraction. g'(x) ||

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Q: Evaluate the integral. |cos *x sin xdx Scos 4 cos "x sin xdx =

A: To find the value of given integral .

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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Q: Evaleuate use integration by-lacts.

A: ∫x2e-3xdxUsing integration by parts

Q: (3 Find the determinant of the matrix 1 -4 D -2 ) 10 ) -10 2.

A: Given problem:-

Q: Maximize the function f(x, y) = 3xy– 4x² – 3x – 5y + 12 subject to the constraint 3x + 4y = 5 Find…

A: To find the maximum of the given function wuth the given  constraint .

Q: a.) Evaleiate. (6tanx dx

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Q: S(2x – 3) (3x + 4)dx

A: To evaluate the given integral.

Q: Exercise 2: Determine the measures of the numbered angles in the following figure 6 5 92° 1 b.

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Q: Find the equation of a curve going through the point (3, 7) and having slope 4x² – 3 at (x, y).

A: Given ,Slope of curve is 4x2-3Thereforedydx=4x2-3Taking integationon both…

Q: 4.1: 8) A street light is at the top of a 15 ft tall pole. A woman 6 ft tall walks away from the…

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Q: A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a…

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Q: Suppose that f and h are integrable and that: L f(x) = -1, f(x) dx = 5, h (x) dx = 4 , Find: %3D %3D…

A: Answer and explanation is given below..

Q: 4. Let f(x, y) be a function defined on a disk D not containing the origin which is given by f(r, y)…

A: See the answer below

Q: Use Lagrange multipliers to find the indicated extrema of f subject to two constraints, assuming…

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Q: Suppose that f and h are integrable and that: i fx) = -1, f(x) dx = 5, h (x) dx = 4 ,Find: a. S–2…

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Q: 4.7.8

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Q: . What is the largest area of a rectangle that could be inscribed in a semi circle having a radius…

A: We have to find largest area of rectangle that can be inscribed in a semicircle having a radius of…

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of PQ.…

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Q: f) 3rd derivative of y : sin 3x g) Find if yVx – 8 = xy +2. if yvx – 8 = xy + 2. dx

A: Note: As in questions d and e no instruction is given solved f and g for you.

Q: A police car is located 60 feet to the side of a straight road. A red car is driving along the road…

A: The police car and the red car are at the twovertices of a right angle triangle with legs of200 feet…

Q: Let A = and B = . Determine the following: (d) A x B (e) two unit vectors perpendicular to B and A

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Q: 3 5 dx

A: To calculate the value of the given integral.

Q: A region bounded by f(x) = x², y 0, and x = 4 is shown below. Find the volume of the solid formed by…

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Q: Given that f(m) = a"h(x) h(- 1) = 4 h'(-1) = 7 Calculate f'(- 1).

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Q: Suppose a pollutant is seeping into the ground near a dump site at the rate of 2800 f(t) : (æ +…

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Q: Evaluate the integral by interpreting it in terms of areas. (10 – 5x) dx

A: Explained below

Q: x2 dy dx2 d²y dy + 2y = 5x° cos(x) 2x Jx - dr solve the equation by undetermined coefficients method

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Q: Find the interval of convergence of (х — 5)" In (8n) n=2 (Use symbolic notation and fractions where…

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. dx 4 - 9x2 ... dx %3D…

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Q: The half-life of caffeine in the body is approximately 5 hours (Brachtel and Richter, 1992). If you…

A: Here, given that the half-life of the caffeine in the body is 5 hours and P0=50 mg. Now, we have:…

Q: Suppose A is the matrix for T: R-R relative to the standard basis. Find the diagonal matrix A' for T…

A: We have to digonal matrix A`

Q: Consider the angle shown below that has a radian measure of 0. A circle with a radius of 3 cm is…

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Q: Evaluate the integral using integration by parts. cos

A: We can solve as follows