Find the work done by F over the curve in the direction of increasing t. F = 10zi + 10xj +10yk, r(t) = (sin t)i + (cost)j + tk, 0≤t≤2 The amount of work done is (Type an exact answer, using as needed.)

Q: We need to use implicit differentiation in these rates of change problems because we generally have…

A: To determine whether the following statement is true or false.We need to use implicit…

Q: 2 2 1) (i) Show that F= 3 xy³i + 3x²yj is a conservative vector field. (ii) Find a potential…

A:

Q: Find the equation of the tangent line to the graph f(x) = cos(x) + x at the point (0, 1).

A: As we know that, The slope of the tangent line to the given curve is equal to the derivative of the…

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A:

Q: Let f(x) = 3x² - 6 and let g(x) = 5x + 1. Find the given value. f[g(-1)] f[g(-1)] = (Type an integer…

A:

Q: 2.10 write as single fraction 6/ x(x-2) - 5/x + x^2/x-2 check your answer by plugging x=1

A:

Q: 2. Find the degree 3 Taylor polynomial of f(x) centered at r=0 = X (1+x) ³/2

A: solution is given below,

Q: 2/5 Find the cost function if the marginal cost function is given by C'(x)= x + 9 and 32 units cost…

A: To determine the cost function

Q: If $800 is invested at interest rate i, compounded annually, in 4 yr it will grow to an amount A…

A: dxndx=nxn-1given  A=800(1+i)4

Q: The marginal profit in dollars on Brie cheese sold at a cheese store is given by P'(x)= x (50x² +…

A:

Q: Find the interval of convergence of the series

A: Given : Ratio test

Q: 39 Find the value of c that satisfies Rolle's theorem for f(x) = 2x^4 -16x I 5. You are a…

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

Q: Given the series: k=1 4 k(k + 2) does this series converge or diverge? converges O diverges Or If…

A: Given ∑k=1∞4kk+2

Q: Find an equation of the tangent line to the curve x² + cos(y) = 1 at the point (1,5).

A: NOTE: Refresh your page if you can't see any equations. . the given equation is  and the given…

Q: Compute the general term an of the series with the partial sum 9 us an - - 9 = n " n> 1. If the…

A:

Q: Determine the general/particular solution (whichever applies): y'-6y"-3-cos(x) 2 y=c₁+₂x+cze…

A:

Q: Use the fundamental identities and simplify the expression sin² x (cot² x + 1) to get a numerical…

A:

Q: 9-10 Use the Midpoint Rule with n = 4 to approximate the integral. tare ople setugmos B 8 • f₁x² dx…

A: Use the Midpoint Rule approximation formula.…

Q: The equation of the ellipse that has a center at (6, 1), a focus at (10, 1), and a vertex at (1, 1),…

A:

Q: K The equation of a hyperbola is given. Complete parts (a) through (e). (a) Find the vertices, the…

A:

Q: write as a single fraction  x 3 - y 4 + x^2 2y (those are supposed to be fractions)  Check your…

A:

Q: 7 Find T, N, and k for the space curve r(t)=7i+j₁t> 0. T(t)= N(t) = i+ 1-1² 4 √√₁+1²-1² +t j 4…

A: Solve the following

Q: a) Convert a Cartesian equation to parametric equations x² - y² = 4

A: Given :

Q: Use the trapezoidal rule with n = 4 to approximate S 1 cos(x) X dx

A:

Q: Find fxx fxy, fyx and fry for the following function. (Remember, fx means to differentiate with…

A: A detailed solution id given below.

Q: a. The points (3,-1,2) and (-1,3,-4) are the endpoints of a diameter of a sphere i. Determine the…

A: Please find the answer

Q: Rewrite the expression without using the absolute value symbol, and simplify the result. |12 + x| if…

A:

Q: Determine the area of the region bounded by y = Area = 1 and y = X on the interval [1,10].

A: To find the area bounded by the given curves.

Q: What is the interval of convergence of a power series? How do you find it?

A:

Q: (a) Identify the vertex, value of p, focus, and focal diameter of the parabola. (b) Identify the…

A:

Q: Change from degrees to radians. 10) 875°

A: we know that    1°=π180 radian

Q: Calculate the indefinite integral Ivio + C 3dt 16- 36t²

A: Answer is in step 2.

Q: Find the nth term of a sequence whose first several terms are given. -2, 4, 10, 16, ... an 6(n − 8)…

A:

Q: Express the limit as a definite integral on the given interval. lim. Σ (x2 + 4x, n→∞ -Ax, [1, 9] 8…

A: Given: limn→∞ ∑i=1nxi*xi*2+8∆x   ,            1,9.

Q: Approximate the area under the curve graphed below from x=2 to x = 7 using a Left Endpoint…

A:

Q: Find the area of the region enclosed by the given curves. 1. y = sin x, y = x, x = π/2, x = π.

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 5 Given sine = and cose: 13 1+ 5 13 5 13 5 13 12 5 0₁4 (3) (4) 1+ 13 13 12 13 12 12 13 13 = 1 =1 12…

A:

Q: 1. Consider the vector-valued function F(t) = sin(2t) t (2,1,-2), a) Find the domain of F. b) Show…

A:

Q: Evaluate. (Be sure to check by differentiating!) X (6-x²)7 dx X (6-x²)7 (Type an exact answer. Use…

A:

Q: Calculate the iterated integral. 5) (0/1)(0x) cos(x²)dydx

A:

Q: Regions in Polar Coordinates In Exercises 1-8, describe the given region in polar coordinates. 2. X

A: Consider the figure below:

Q: What is an example of Leibnitz notation that's used to indicate rates of change? (See Strategy for…

A:

Q: Suppose you deposit $1000 at 5% interest compounded continuously. Find the average value of your…

A:

Q: Below is the graph of y = x² + 5. 301 20- 10- -3 -2 -1 0 1 The area bounded by y = 2 3 4 5 22 +5 and…

A:

Q: =function f(x) Find f'(x). x x+2

A:

Q: Find 11 circular arcs. a. f(x) dx for each graph of y = f(x), where f(x) consists of line segments…

A: Part b of the question has been solved as per the requirement of the student.

Q: Find the largest possible area for a rectangle whose perimeter is given at 16 ft.

A:

Q: Problem 5. series: ∞ mn n! (2) Σ n=0 (0) Σ n=1 (x – 3)n η Compute the radius and interval of…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: x = y² and x = 9 YA 4 2. 0 -2- 4 x = y² 2 4 6 + 8 x = 9 10X

A:

Q: suppose that Σ n=1 sum of the series: A. B. an = - 7 and Σ. (2an + - 50) - n=1 Σ (2an + 5bn) : = n=2…

A: The given data is: ∑n=1∞an=-7∑n=17bn=7a1=-6b1=3  A) To find the value ∑n=1∞2an+-5bn