7 5 5. sec '(In t) tan° (In t) dt t

Q: Find the first and the second order partial derivatives of the following functions.

A: Explained below

Q: Describe the graph of the equation. r = -6i+ (1 – 1? )j + t k O It is a parabola in the plane z =…

A: Given problem:- Describe the graph of the equation.   r = - 6i + (1 - t2) j + tk

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) x3…

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Q: Evaluate the integral dx (6х + 5)? y making the appropriate substitution: u = dx (6x + 5)2 II

A: Given query is to find the integral.

Q: Evaluate the indefinite integral. x2 dx 0.2x3 + 2.7 + 2.7

A: topic - indefinite integral

Q: 11. If f"(x)=-4sin 2.x, f(0)=0and f'(0) =2, find the value of f 4 %3D

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Q: In constructing an open rectangular box from 48 ftf of material, what dimensions will result in a…

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Q: 4- Find lim,: ( -) 10 20 (You cannot use numerical table method). tan(2)-1 tan?(2)–1)

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Q: st Show all -. If s = 1+3i, t = 2 – 5i and u =– 2+ 5i then calculate your working. Write your answer…

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Q: (6) At the start, an experiment records 1 gram of bacterial culture, and the culture's weight is…

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Q: Q9. Find the equation of the tangent plane to f(x, y) = x In(y) + x²y+3 at the point (x, y) = (2,…

A: Consider the equation of the form          F(x,y,z) =0 then the equation of the tangent plane to the…

Q: In order to sketch the graph of f'(x), we must have a formula for f(x).

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Q: Calculate the derivative (implicit derivative): y + 19xy = Cos(7x – 5y) %3D |

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Q: (d) 10*+3 = 62r

A: Given,  10x+3=62x

Q: QUESTION Determine the length of the missing side of the right triangle below. Round your answer to…

A: The given triangle is:

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: The demand curve for a certain product is given by p(q) = 541 - q. The supply curve is given by p(q)…

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Q: f(x,y) = 2y3–3y² – 12y+2x2 – 4x+2.

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Q: 12 12 f(x) dx = 16 and 9. If f(x) dx = 5, find the following. %3D f(x) dx

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Q: dy Suppose 9 x²– 2 ( 3 x³-2x+3) and y(1) = 3. dx What is y(2)?

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Q: Suppose the function f is continuous on the closed interval (1, 2], f(1) = 5, and f(2) = 9. Then,…

A: Intermediate value theorem: if “f” be a continuous function over a closed interval [a, b] with its…

Q: q² In(2x)dx

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Q: Find the derivative of f(x,y) = x +y in the direction of the unit tangent vector of the curve r(t) =…

A: The unit tangent vector T→t can be defined as the unit vector in the direction of the velocity…

Q: Find an equation of the plane. The plane that passes through the point (3, 4, 5) and contains the…

A: Given

Q: Where does the line through (1, 0, 1) and (3, –3, 4) intersect the plane x + y + z = 6? (x, y, z) =…

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Q: ||r(t) × r"(t)|| ||r"(t)||³ Use the formula k(t) = to find k(t). r(t) = eti+ej

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Q: In Exercises 1-4, solve the given initial-value problem. (For Exercise 3, you may "complexify" the…

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Q: A rotating light is located 15 feet from a wall. The light completes one rotation every 5 seconds.…

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Q: To evaluate the integral xe2" da using integration by parts, the best choices for u and dv are: u =…

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Q: -2ry f (r, y) = e

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Q: 3 Ay 10- Find equation of tangent line at the point (0, 7) for Cos (7x - y)

A: Solving

Q: An object with an initial velocity of v(1) = 2 has an acceleration of a(t ) = %3D ( 2t – 1) What is…

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Q: Select the expression that is equal to 10P7

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Q: Determine whether L'Hospital's Rule applies to the limit below, then evaluate the limit 33 – 2x +5…

A: Given query is to find the limit.

Q: Consider the region bounded by x = 3y and x = y^3. A solid is formed by rotating the region about…

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Q: dy Find dx 4t t dt + 2 y = dt - t° + 2 - 3 6. dy dx (Simplify your answer.)

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Q: Q15. Find the Maclaurin series representation for each of the following functions. For each series:…

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Q: 1 Find Vf if f = 2 /x²+y² +z?

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Q: The SMPT group at UB sells past final exams packages (small and large) for $2 and $3 respectively.…

A: topic - linear equations

Q: Determine whether the geometric series is convergent or divergent. If it converges, find its sum. 80…

A: Geometric Series : (3/4)0 + (3/4)1 + (3/4)2 + (3/4)3 + (3/4)4 + ........... 1 + 3/4 + 9/16 + 27/64 +…

Q: Use Newton's method to approximate a root of the equation +x + 4 =0 as follows. Let 1 = - 1 be the…

A: The given equation,    x3+x+4=0

Q: 1 The series k=1 10n converges. True False

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Q: 10 Consider the function f(z). 6. Let F(r) be the antiderivative of f(z) with F(1) 0. Then F(z)

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Q: Verify Green's Theorem by evaluating both integrals aN y? dx + x² dy = /, J da ay ax for the given…

A: We have to verify the green theorem for the

Q: e Newton's method to approximate a root of the equation 5x+ 7x +3 = 0 as follo 1 = -1 be the initial…

A: answer is in next step

Q: Suppose that total cost is given by C(q) thousand dollars when q million units are produced. What…

A: Given query is to interpret the marginal cost C′(25) = 4.

Q: 1. Determine the convergence or divergence of each of the following sequences {a, }. sequence.…

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Q: The difference between f'(3) and f'(x) is that f'(3) is a numerical value and f'(x) is a function of…

A: Explanation of the answer is as follows

Q: Find an equation of the plane. The plane through the point (7, 0, 5) and perpendicular to the line x…

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Q: 2. (6x-2) dy d2

A: Given query is to find the value of the integral.