-) 1 = dx x (1-√x)²

Q: Determine the real number a such that u x v and i are orthogonal, where u = 5i + j - 9k and v = 6i -…

A:

Q: Solve the differential equation dy dx y²+7xy+16x² x² O a. x - y = O b. x + y 5 (y + 4x) In y O C. X…

A:

Q: Find the following limit. lim

A:

Q: Suppose that f(x, y) = 5, and D = {(x, y) | x² + y² ≤ 1}. Then the double integral of f(x, y) over D…

A:

Q: Evaluate (² + y2) ds, C is the top half of the circle with radius 2 centered at (0,0) and is…

A:

Q: Compute the given integral. 11z - 2 11x² - 4x + 5 -dr +C

A:

Q: Answer the following True or False. If g(x) is a continuous function and h(x) is differentiable such…

A:

Q: Let v = 37 - 47 + 2k. Find ||||. Check Answer

A:

Q: Find the linearization of the function f (x) = x6 at x = 1. L (x) = Using this linearlization, f…

A:

Q: 14-Consider the Lie nard equation - (u-x²)x + x = 0. The Jacobian matrix for the linearized system…

A:

Q: Q3. Find the distance between the points AB and BC where A is (2,1,0), B is (-1,3,1) and C is (-1,…

A: The points A2,1,0, B-1,3,1 and C-1,0,1 we have to find the distance between the points AB and BC…

Q: Find the arc length (s) of the curve r(t) = (est, -2e5t, 3e5t) for 0 ≤ t ≤ In (2) 8=

A: The arc length s of the curve r→t=x(t), y(t), z(t) for a≤t≤b is given by s = ∫abx'(t)2+y'(t)2+z'(t)2…

Q: 1. Which of the following functions grows the fastest as x goes to infinity? O 2x О 3x O Ox20 ex

A:

Q: Evaluate the definite integral. 1. 2 cos-¹(x) √1-x² dx

A: Given Problem:- ∫-11-2cos-1x1-x2dx

Q: Let f(x) = 10x + 12 - 9e. Then the equation of the tangent line to the graph of f(x) at the point…

A: given f(x)=10x+12-9ex

Q: Consider the vector whose initial point is P(-6, 6) and terminal point is Q(5, 3). Find the position…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Find the average value of the following function where 9 ≤ x ≤ 11: f(x) = X C 81 dx

A:

Q: 5. The movement of the crest of a wave is modelled with the function h(t) = 0.2 cos(4t) + 0.3…

A:

Q: Evaluate [/FO f(x, y, z) ds. f(x, y, z) = xy Z S: z = x² + y², 9 ≤ x² + y² ≤ 81

A:

Q: d) Hence form a conjecture for the derivative of functions in the form y = (ax + b)². e) Prove your…

A: As you have mentioned I am answering Question (d) and Question (e)

Q: Evaluate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

A: Given: ∫05|10x-5|dx

Q: Find the indefinite integral on the domain of positive real numbers. Enter an exact answer. Remember…

A:

Q: Find the linearization of the function f (x) = x³ at x = 1. L(x) = Using this linearlization, ƒ…

A: Answer is in next step.

Q: x²+1 lim x-5 √2x+2-2

A: We have to evaluate the limit.

Q: Problem 1. You are fencing in an area next to your house so your cats can lounge outside. The cat…

A: We have given the length of material that is avialble for fencing is 27 feet.

Q: For the function f(x)= −2sin(x−3π/2), determine its amplitude and period, and then graph it for two…

A:

Q: 1. Let f(x, y) = y²exy. (a) Find the normal vector to the graph of f(x, y) at (0, 1, 1).

A: Please see the below picture for detailed solution.

Q: Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented…

A:

Q: In this question, consider the vectors 10 8 V1 ~- - ( ) - ~- - ( ) - - - () ---- () v2 = V3 = b and…

A: The objective of the question is determine the coefficient matrix" A" without simplifying.

Q: y = (In x)* xln x

A: Explanation of the answer is as follows

Q: What form of the particular solution is appropriate for the differential equationy'' - y'=4+4e*.

A:

Q: Evaluate the integral: Fa ○ x = 6 sin(0) ○ x = 36 tan(0) 28 x²√x² + 36 dx (A) Which trig…

A:

Q: 14. Given the graph of g(x), Draw the graph of g-¹(x). Show your strategy for drawing the graph of…

A:

Q: √√√x- S: z 12, x² + y² ≤ 1 Evaluate (x - 2y + z) ds.

A:

Q: Solve the differential equation (2x + y) dx - O a. 5x+10y + In |10x O b. O c. 5x O d. 5x (4x + 2y -…

A:

Q: Let r(t) = (-5t¹-2, - 5e³t, 2 sin(3t)) Find the unit tangent vector T (t) at the point t = 0. Round…

A: This question is related to differentiation, We will solve it using given information.

Q: (a) Consider the power series Show that B(x) converges for all x. B(x) = Σ n=0 (-1)η 2η 22n (n!) ²

A:

Q: 1. Evaluate the following matrix operation: [5 3 a. A = 1 -4-3-1 L2 b. |B| C. C = 31-33+231 5+20 0 1…

A:

Q: Let f(x) = ln(x² + 16x + 68) f'(x) =

A:

Q: 1.2: The solution of (Se*-3)³ = 32 is a) In 3 b) 2 c) 1 do e) None of the above

A: Explanation of the answer is as follows

Q: 4. 5⁰ -x² xe dx

A: Given Problem:- ∫0∞xe-x2dx

Q: 1 Find the Taylor Series generated by f(x) = (7-X)⁹ at X=6 9 (7-x) 10 f'(x) = 90 f"(x) = (7-x)" f(x)…

A:

Q: = Approximate the area under the curve y with 4 subdivisions. x³ from x = 2 to 4 using a Right…

A:

Q: Please show your answers to at least 4 decimal places. Find the directional derivative of the…

A:

Q: Solve the differential equation dy dx y+√√x²+y² X O a. y² = 2x-1 O b. x2 = 2y-1 O c. √x² + y² O d.…

A: To solve the given differential equation.

Q: 8. Find the stationary points of the following functions and classify them as relative maxima,…

A:

Q: What is correct form of the particular solution associated with the differential equationy'''=8?

A:

Q: 8. Give examples of sets of three vectors that are a. Collinear b. Coplanar c. Not coplanar Explain…

A: Solution: a) Collinear : Two or more vectors are called collinear when they are parallel to the same…

Q: Let f be a continuous function such that D -3 f(x) dx = F 3. What is the value of f(x) dx = -2 and…

A:

Q: 5) Show that to order O(h²), the central difference formula for the partial derivative მ3u(x,t) əx3…

A: