¹ // x² + y² + 2² dV, where E is the ball: x² + y² + z² ≤ 16. Use spherical coordinates to evaluate the triple integral

Q: The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure…

A: Question is solved.

Q: Find the area under the curve y Т over the interval [1,4]

A: Topic = Area

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

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

Q: y (2x + y 2) dx O a. y (2x + y) = Ce - 2(x + y) dy = 0

A: y2x+y-2dx-2(x+y)dy=0 Lets check for exactness.…

Q: Which of the following functions will have a dashed line for the graph? y ≤ 4x^2 + 1 y = 4x^2 + 1…

A: Question : Which of the following functions will have a dashed line for the graph? 1. y ≤ 4x^2 + 1…

Q: Use 1st and 2nd derivatives, sketch the graph of given function 2x x² - 1 f(x) =

A:

Q: 1. The graph of f '(x) is continuous and increasing with an x-intercept at x = 0. Which of the…

A: Topic- application of derivatives

Q: For the function f(x,y) = 8x² + 7y², find f(x + h,y)-f(x,y) = h f(x + h,y)-f(x,y) h

A: Given, f(x,y)=8x2+7y2

Q: Consider the function f(t) = 5 sec²(t) — 9t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A:

Q: Evaluate the following integral over the Region R." (Answer accurate to 2 decimal places). S S 4(x +…

A:

Q: 1 2 ¹/² (²1-5) dz. Write a limit using summations that would equal

A:

Q: Q2. Find the second order partial derivative of x² - y² + 2xz - xy + yz.

A: The given function is x2-y2+2xz-xy+yz.

Q: Je²² e² sin (e)dr

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 1. A particle moving along in a straight line with a uniform acceleration covers 72 cm displacement…

A:

Q: (2x+5)³(52²-2x) 4. Use logarithmic differentiation to find the derivative of the function y = √2x+5

A:

Q: The area of a square is increasing at a rate of 56 centimeters squared per second. Find the rate of…

A: Given data÷ Rate of change of area  =dAdt=56cm2/s Side of square =a=4cm We need to find dadt=?

Q: Find a vector with initial point (-4,-2, 1) and terminal point (-12, 5, -8). Then find a unit vector…

A: Given problem:- Find a vector v→with initial point -4,-2,1 and terminal point -12,5,-8.Then find a…

Q: I have a question about the problem solved…

A: The explanation of your query can be solved using the concept of function.

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

A: Given Problem:- ∫-11-2cos-1x1-x2dx

Q: Q-3: a) b). Using logarithmic differentiation, find the derivative of -3x√2x-5 (6-5x)4 - 34x = 0.…

A:

Q: Solve the differential equation (3x² - 2y²) y' = 2xy; y (0) = -1 O a. y² = 2x²(x + 1) O b. x² =…

A:

Q: Let f(x) = x^2 - 4x + 1. What is the equation of the tangent line to f(x) at x = 2? Use the limit…

A: Please see the below picture for detailed solution.

Q: Find the values of x, y and z that correspond to the critical point of the function: f(x, y) = 4x² +…

A:

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: Find the acceleration vector for the position vector r(t) = (sin(11t), 4tº, e -2t). x component = y…

A: We need to find acceleration vector.

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 fxx (x,y), fxy(x,y), fyx (x,y), and fyy(x,y) for the function f. f(x,y) = 5x e 5xy fxx (x,y) =…

A: The given function is: f(x,y)=5xe5xy

Q: y = [x + (x + sin² x)³]4 I

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: 1. Determine if the following limits exist: (a) (a) lim (x,y)→(0,0) lim (x,y)→(0,0) ₂2 x² + y² 1 —…

A:

Q: Let f be a continuous function such that 10 9 f(x) dx = 5. What is the value of f(x) dx = -6 and…

A:

Q: Solve (2y² + 3xy a. - 2y + 6x) dx + x (x + 2y x² (y² + xy + y + 2x) = C b. O c. x² (y² + xy y² (y² +…

A:

Q: S dx 3 cos x-2 sinx+3

A:

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

A:

Q: Solve the differential equation xdæ +sin? (%) [yda — xdy]=0 2x a. 4x In 2y + x sin (2²) = 0 O b. 4x…

A:

Q: Write a limit using summations that would equal So 0 tan (2x) dx.

A: The integral is given by ∫01tan2xdx To evaluate: The limit using summation that is equal to the…

Q: Find the second derivative of the vector-valued function r(t) = (4t+ 3 sin(t))i + (5t + 3 cos (t))…

A:

Q: Let f(x, y) = 2e sin(4) of д х of dy Check Answer

A:

Q: 2x lim(x,y)→(0,0) x² + x + y²

A:

Q: Find the distance between point A(3, 4, 4) and the line of parametric equations x = -1-t, y = -t, z…

A:

Q: If C(x) = n=0 ∞ n=0 2n + 1 2n + 2 2n ²n and S(x) = ∞2n+2 2n + 3 n=0 -x²n+ find the power series of…

A: The given power series, Cx=∑n=0∞2n+12n+2x2n and Sx=∑n=0∞2n+22n+3x2n+1

Q: Find two positive numbers with product 625 and whose sum is a minimum. Enter your answers in…

A:

Q: Suppose R is the solid bounded by the plane z = 5x, the surface z = x², and the planes y = 0 and y =…

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: 4. If ricost cosh t+j sint sinh t, where i and j are constant orthogonal vectors prove that (a)…

A: Given r = i cost cosht + j sint sinht

Q: 2. Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives få and fy at the…

A:

Q: 7. Find: y = In dx √6x-5 [ Lex (x+1)³.

A:

Q: dx 3 sin x-6 cos x

A:

Q: Let f be a continuous function such that 10 1 of f(x) dx? 4 What is the value of 4 8 f(x) dx 10 1²°…

A:

Q: Solve (2y³ – x³) dx + 3xy² dy=0; y (1) = 1 O a. x² (5y³ x ³) = 4 b. ? (5y® — g - 23) x³) = 0 ○ c. x²…

A: