Consider the vector field F = F(t) = t²i+t³3 0 Evaluate 1² F. dr along the curve C:

Q: Find the length of the curve for 1 ≤ t ≤ 3. x== - (3+t), y = (2 + 3t), z = 5 - 4t, length = (Think…

A: For the given parametric curve we have to find the length of the curve. We can easily find the…

Q: Find if the series converges and if it does and you can find the sum, find it: 2. Σ00 (2)

A:

Q: Q5 Let g(z) = 10+ f(f) dt where the graph of S(x)S is given in the graph below. f(x) XX Select the…

A:

Q: 28) About the y-axis 3- 2- 1+ x = 3 y=2+x²/9

A:

Q: What are the domain, range, and period of the function Explain how you determined your answer for…

A:

Q: Find the volume bounded by the paraboloid z = x² + y² and the sphere x² + y² + z² = 2 using…

A:

Q: Evaluate the integral. Check your answer by differentiating. (Remember the constant of integration.)…

A:

Q: Find the gradient vector field of f(x, y, z) = 2x¹ + 8y³ + 3z5

A:

Q: Evaluate the integral. *98 + x² 1⁹8 VX dx

A:

Q: Find the point where the lines (t) = (0, 1, 1) + t (1, 1, 2) and (t) = (2,0, 3) + t (1, 4, 4)…

A:

Q: Starting from the point (−4, −2, −4) reparametrize the curve in terms of arclength. r (t (s)) = i+ r…

A: Arc length.

Q: Use the graph of y=f(x) shown to the right to graph the following function g. g(x)= -f(x-4)-1 Choose…

A:

Q: 3 | (x + 7)10(5x − 1) (8x + 8)² Use logarithmic differentiation to find the derivative of f. Let…

A:

Q: 4.Describe the largest set S on which it is correct to say that f is continuous b. f(x,y)=(1+x² +…

A:

Q: f(x, y) = V 2 2 3x² + 4y²

A:

Q: b) Find an equation of the plane that contains the two vectors given below and contains the point…

A:

Q: Solve the initial value problem. dr Differential Equation: Initial Condition: r(0)=3i-5j O A. r(t) =…

A: This is a variable sepration differential equation

Q: Replace the Cartesian equation x = 19 with an equivalent polar equation. The equivalent polar…

A:

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. h'(x) =…

A:

Q: Write the expression in rectangular form, x + yi, and in exponential form, re (√2-1) 6 The…

A:

Q: Q4.3 The general solution of dy dx 5y is

A:

Q: Suppose the Sunglasses Hut Company has a profit function given by P(q) = -0.02q² + 3q - 41, where is…

A: Given the profit function.

Q: Suppose that f(x, y) = e/y at which {(x, y) | 0 ≤ y ≤ 2,0 ≤ x ≤ y³}

A:

Q: 1.Find all the first partial derivatives of each function a. f(x,y)=e* b. f(x,y)=√x² - y²

A: *Note – when finding the partial derivative w.r.t on variable, other variable consider as constant.…

Q: Simplify the expression. √108r4+√48x4 Enter the exact answer. Hints: 24 • You can write exponents…

A:

Q: A cylindral drill with radius 3 cm is used to bore a hole through the center of a sphere with radius…

A:

Q: Replace the Cartesian equation x² + y² = 49 with an equivalent polar equation. An equivalent polar…

A: Polar system.

Q: Use matrices to solve the system of equations. (Use the parameters x, y, and z as necessary. If…

A: The given system of equations, 4x-3y+3z=45x+y-4z=19x-2y-z=5 We have to find the solution to the…

Q: Express the vector as a product of its length and direction. 21+4j+4k O A. 6 OB. 6 18 + gi+? OC.…

A: The given vector is  2i + 4j + 4k we have to express vector as a product of its length and…

Q: 5. Does the sequence {{²} (−1)” n diverge? Explain converge or

A:

Q: If the marginal revenue (in dollars per unit) for a month for a commodity is MR = −0.6x + 23, find…

A: The total revenue function from the marginal revenue function is: Rx=∫Mxdx

Q: Let F(x, y) - (5,-8y) and let R be the rectangle with vertices (0,0), (8,0), (0,2), and (8.2).…

A:

Q: Sketch and find the area bounded by y=&sect and y=-4 sin²t:

A: While plotting the graph of  y=12sec2(t) and y=-4sin2(t), we cannot find any intersecting points. So…

Q: If Ꮎ = sin(0) 5п 4 = cos(0) = then Give exact values. No decimals allowed!

A: given,  θ=5π4

Q: nd [f6d. 6dA over the region R = {(x, y) | 0 ≤ x ≤ 2,0 ≤ y ≤ 6} by indentifying it as the volume of…

A:

Q: Let P be the plane in space that intersects the x-axis at 2, the y-axis at -2, and the z-axis at -4.…

A:

Q: If r(t) = cos(-3t)i + sin(−3t)j – 10tk compute r' (t)= i+ and fr(t) dt= with C a constant vector. i+…

A: r(t)=cos(-3t) i+ Sin(-3t) j-10tk

Q: 1.Find the indicated limit or state that is does not exist lim(3x²y — xy³) a. b. (x,y) →(1,3) lim…

A:

Q: Evaluate fry³dz ry dx + x³dy, where C is the rectangle with vertices (0,0), (6,0), (6,2), and (0,2)

A:

Q: Consider the vector field F Evaluate Xx 3 70 1.² F. dr along the curve C: F(t) = 5 cos(t)i + 5…

A: Change the integral in terms of 't' .

Q: Question What is lim x → +∞ I -? 10 ex -1

A:

Q: The area of the surface generated by rotating the curve y = 1 -e ¹, where -3 ≤ x ≤ 3, about the…

A:

Q: Consider the vector field F = Evaluate r(t) = t²i+t³j, 0≤t≤3 Calculator ·[F. Check Answer F. dr…

A:

Q: Find AB given that: 2-4 and B= 0 -2 3 8 170 A = 4-[-33] -3 5 11

A: Given data

Q: The gradient of f(x, y) = ² * sin(2y) at (x, y) = (2, 1) is defined as followed: Vf(x, y) = (fz(2,…

A:

Q: Lyds, yds, C: x = t², y=t, - 2 ≤ t ≤ 8 Evaluate Calculator Check Answer D

A:

Q: Let F(t) = (3t³-3, 4e², - sin(4t))

A:

Q: 3) Consider the series 33-n 5-n+1 i) Show that the given series is geometric series. ii) Determine…

A:

Q: 5. Use the limit comparison test to find if the series converges: 201 n+5 n³ −5 )

A: Series is summation (n-5)/n3-5

Q: Question 11 Let R be the region bounded by y=x, y=2x, x= 1, x=2 6 y RX² + y² - SS₂² and I= - dA. b)…

A: I=∬R6yx2+y2dA The region bounde by y=x,y=2x,x=1,x=2