6. Let A= (1, 2, 0), B = (3, 4, -1), and C= (4, 5, 2). Find the exact value of the distance between point C and the line passing through points A and B. Use vector operations.

Q: In Exercises 101-108, assume that each sequence converges and find its limit. 101. a₁ = 2, an+1 102.…

A: The objective of the question is determine the limit of the given sequence.

Q: Find the mass of the portion of a sphere in the first octant with radius 1 and density function…

A:

Q: ³ sin y - 3) = √10 ² Let f(x, y) dt 1 + cos² (t) 16 Then f (2, π/6)=

A:

Q: Differentiate Quident rule 4x² + x √x

A:

Q: T² T³ T Y pln(y+z) e dxdzdy = [Show your solution.]

A:

Q: In the following limit, identify f(x), a, and L. Select the correct answer below: O f(x) = -x + 2; a…

A: A detailed solution is given below

Q: 2.1 2.3 2.4 2.5 1. 2. 2.1 QUESTION 3 2.2 2.3 Sketch the graphs of fand g on the same set of axes for…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Consider vectors A-40+30) and B-4.02 +8.03. ▾ Part C If the direction (but not the magnitude) of B…

A:

Q: Let R be the region bounded by x = 1-y², x = 2 + y², y = -1, and y = 1. Find the volume of the solid…

A: The symmetry means we can integrate from 0 to 1 and double the answer. x = 2 + y² opens right and…

Q: J x³x²7x + 13 x² - x - 6 -dx

A: Please see the below picture for detailed solution.

Q: Given the complex-valued function 1+z z² Evaluate f (¹) (A) -4-3i (B) - f(z) = (C) −¹+²i (D) none of…

A:

Q: x²y (z,y) (0,0) x4 + y² If it exists, find lim Answer: Write DNE of the limit does not exist.

A:

Q: Both Trapezoidal Rule and Simpson's Rule give the same result when applied to any polynomial of…

A:

Q: (y − √√x² + y²) dx − xdy = 0 when x = x √(x² + y²) = 1 Option 1 y-√√(x² + y²) = 1 Option 3 y —…

A:

Q: In 1991, there were 41,628 shopping centers in a certain country. In 2001, there were 48,434. (a)…

A:

Q: S x² + x x³ − x² + x - 1 - dx

A:

Q: The figure shows a region in the complex plane. Write an algebraic description of the shaded region.…

A: We have that the center is 4+i. So, we have the LHS as |z-4-i|. We see that (7, 0) is on the curve.…

Q: Bernoulli Differential Equation: Find the general solution 2 = x³y4 x dy dx y-³ = cx6 + 3²4 2y-3 =…

A: To solve differential equation

Q: For the function f(x) = 7x³ - 2x² + 2x +9, find f''(x). Then find f''(0) and f''(9). f'(x) = Select…

A:

Q: me following limit, identify f(x), a, and L. elect the correct answer below: Of(x) = -x + 2; a = -1;…

A:

Q: Find the integral of the following: 1. tan(x)sec3(x) dx 2. csc4(x)cot5(x) dx

A:

Q: Simpson's 3/8 Rule for integration is mainly based upon the idea of O Approximating f(x) by a 3rd…

A: To Find : Idea on which Simpson's 3/8 th rule is based on

Q: Let f(x) = 5x² - 4 to find the following value. f(t+1) f(t+1)= 5t+10t+1

A: Given f(x)= 5x2-4

Q: Solve with solution determine the slope of the tangent line to the curve y=3x2 – 2x at the point…

A: Topic = Derivative

Q: Evaluate the following integral: Ca-ex ·e¯³) dx a. Analytically b. Trapezoidal rule c. Composite…

A: As per our guidelines we are allowed to answer only three subparts of a given question. Kindly…

Q: The solution of differential equation y' + (cot x) y = 3 sin x cos x, x=(0, π). is:

A:

Q: 65. Find the volume of the solid formed by revolving the region bounded by the graphs of y = 3-x²…

A:

Q: X The variable h is the height of the ladder's top at time t, and x is the distance from the wall to…

A:

Q: The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a…

A: To find velocity at time t  and distance travelled during given time interval.

Q: Determine p'(x) if p(x) = (5x)7x and x = 4. Select the correct answer below: 2028 (51n 20) 2028 (7In…

A: Given p(x)=(5x)7x and x=4To find p(x):

Q: Find the exact value. In 3 0 ³ sech 4 x tanh x dx

A:

Q: (i) Determine if the following functions are even, odd, or neither. Show your algebraic…

A: as per our guidelines we can answer only one question hence i am answering question a.), thank you…

Q: - If u = 4j – 2k and v = 27 − j + 7k, find || − 3ủ + 5v||. Select one: O 2√230 O 3√373 O 2√373 O…

A:

Q: @)X = y² + 1₁ x = 0, y = -1 y = 2 The appropriate integrand to find the volume of the solid…

A: Solution is given below:

Q: Problem 4: Find the derivative (f'(x)) of a) f(x) = (x² − 3x)(7x+15), b) f(x) = = x-5 x²-x+7

A: Given f(x)=(x2-3x)(7x+15)DIfferentiate…

Q: Find the area of the region bounded by y=x²-6r+5 and the z-axis. (a) A- 125 3 square units (b) A (c)…

A:

Q: Determine the volume of the solid under z = 4xy + x² over the rectangle R= [1, 2] × [0, 3]. [Show…

A:

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

A: A Sequence is said to be convergent if it approaches some limit. A sequence is said to be divergent…

Q: Q2.B. A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another ticket is…

A: here we have to find probability of given  total ticket = 19  we have to find two ticket both are…

Q: The following differential equation (+1)² + 2²/ x2 dy x² has an order of 02 3 01 = sin x

A:

Q: DETERMINE THE SLOPE OF THE TANGENT LINE TO THE CURVE y=2 – x2 at the point (3,-7)

A:

Q: Use the formula for the binomial series: to obtain the Maclaurin series for V1 + x. Ο 1- O Ο 00 1 +…

A:

Q: A lamp shade is in the form of a frustum of a cone with slant height 7 in., radii of base 3 in. and…

A: The curved surface area of the frustum is given by:                   Given: r = 3 in. R = 7 in. l…

Q: DIFFERENTIAL

A: Please refer to the image below

Q: A Let R be the region bounded by y = √cos x, x = generated when R is revolved about the x-axis. 4'…

A: Follow the procedure given below.

Q: sin r√9+ cos² rdx

A:

Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have…

A: We will use calculus of two variables to find the required information about the function.

Q: 2. Find the first 4 terms of Taylor series for the function (In x4) about x = 3 ?

A:

Q: Maximizing the Volume of a Box An open-top box is to be made from a 30 in. by 40 in. piece of…

A: Let's solve given maximizing volume of a box problem.

Q: Problem 3: Find (i) f'(x) and (ii) f"(x) of the following functions. 6x4-√x , c) ƒ(x) = e4 – 5e-5x -…

A: As per the rules of the company we can answer only the first question and rest can be reposted.