Evaluate the following integral. 2x + 5 2 x + 25 X 2x + 5 2 x + 25 dx dx =

Q: Find y' if 7 y² + sin (3x) = 12-yf

A:

Q: g(x) = ecosh(3x)

A: Solve the given

Q: Evaluate the following integral using integration by parts. f10te' dt OA. 10te¹ + (10te¹) dt OB.…

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

Q: Make an appropriate substitution and then use integration by parts to evaluate the integral. 5x14 ex…

A:

Q: State the equation of the rational functions whose graph is below. y 5+ 4+ 5432 3+ 2+

A: NOTE: Refresh your page if you can't see any equations. . as we can see  from the graph, the…

Q: Step 4 Finally, determine(-3x + 7) and (x + 7) and simplify the result. dx dx 1. du 1 dv + U dx V dx…

A: formulas we use: ddxf+g=dfdx+dgdxddxkx=k; k is a constant.dkdx=0; k is constant.ddx(x)=1.

Q: 20. Evaluate the limit or show that the limit does not exist. Show proper work. sin y cos y ye (a)…

A:

Q: Combine into a single logarithm log3 - 4 log; y + 2 logą z − 2 O 10g3 O log3 2yª O 10%3 gyt 2½ O…

A:

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

A:

Q: (a) d (√1+x²)

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the average value of f over the given rectangle f(x, y) = 2x²y, R has vertices (-3,0), (-3, 3),…

A:

Q: Given the function x³ + y³ = 4, find y' Oy = = Oy = = 0 y = = V Oy =

A:

Q: The corners of a rectangular plate have coordinates (2,2), (8,2), (8,8) and (2,8). The density of…

A:

Q: Evaluate i. Integral 6xln(3x^2+5)dx by selecting and using appropriate substitution.

A:

Q: Solve the inequality. State the solution in interval notation: 6x4 + 12x³ < 48x²

A:

Q: Give the appropriate form of the partial fraction decomposition for the following function. 3x…

A: Topic -Partial fraction decomposition We are given, 3x(x-1)2(x2+3)

Q: Axe - N 6x²

A: Given Function:- y=Axe-6x2

Q: (a) Using your calculus skills, find the equation of the tangent line to the parabola y = 4x² - 2x +…

A:

Q: The average price of a two-bedroom apartment in downtown New York City during the real estate boom…

A: Topic- exponential function and derivatives    We are given, The average price of two bedroom…

Q: A particle moves along the curve implicitly defined by xy¹ - yx4 = x-y2. When the particle passes…

A:

Q: A rectangular poster is to contain 162 square centimeters of print. The margins at the top and…

A:

Q: HW Salve the following equat.i.912.s...... 2. Schichen Ren) dite.

A:

Q: 2. The area of Mammoth Cave Nationc Park in Kentucky is about seventy-four thousand, nine hundred…

A: We have given the area of the which is "Seventy-four thousand, nine hundred thirty and sixteen…

Q: If √x + √y = 12 and y(1) = 121, find y'(1) by implicit differentiation. 11- X

A:

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

A: Given query is to find integral converging or diverging.

Q: The third derivative of the second derivative of y = f(x) is also O y(4) Oy (3) O f(5) (x) O D²y

A:

Q: Step 2 Now write the derivative in terms of x by recalling that u = x³ = x + 8. [eu] = (eu) du dx…

A: I have solved step by step in detail....go through the solution

Q: Solve (√x+x)=√y+y Select one: O a. y (c(1+√x) + 1)² O b. y = (c(1+√x)-1)² O cy=(-c(1 + √x) + 1)² O…

A: The given equation is; [sqrt(x)+x]dy/dx=sqrt(y)+y.

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 4x³ - 6x² -…

A:

Q: Write an equation (any form) for the quadratic graphed below 5+ y = 3 2 1 -5 -4 -3 -2 -1 + -2 -3 1 2…

A: Given query is to find the function of the graph.

Q: How much do the volume of a sphere change with respect to its diameter at the instant, and the…

A: Recall: Volume of sphere, V=43πr3

Q: 4. Find if possible, the absolute max and absolute min. for. on [0₁4 > f(x)= x X-4

A:

Q: Show that the triangle with vertices A, B, and C is a right triangle. d(A, B)2 = 145 d(A, C)² + d(B,…

A:

Q: Solve the given equation.. (x +2)sinydx + xcosydy = 0

A: Given Differential Equation:- x+2sinydx+xcosydy=0

Q: dv 22² = 3/ dt v-1 32 a) Write the given first-order LDE in standard form. b) Solve for the general…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: i. sin³ (r) dr dx ii. (tan(x) dx

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

Q: 12 -1 -2 (x² - y²) dydx O none is correct -8 00 08

A: To solve the given integral.

Q: b. If the surface area of the rectangular box is 24 square feet, find dy when x = dx 2 feet and y =…

A:

Q: Find the parametric equation for the line where the planes 4x + 6y + 2z 12 and 2x - y + z = 2…

A:

Q: Find the derivative of the functions f(c)=xsinh-1 8/3 √9+x²

A: see below the answer and calculation

Q: 22) The given equ" of the circle (x+12) ² + (y + 5) ² = 169 Here centre of the circle ins (-12,-5)…

A: The following is the digital format of the given text.

Q: Calculate the partial derivatives of a function of two variables. Given f(z, y) = 10 + 4y + 7zy,…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: y = 5x³

A:

Q: dy 9. Given the curve xy - y³ = 7, find dx y [A] xyz [B] 3y x-y² y [C] -²/3 [D]x-3y [E] y x-3y²

A: On solving this we will get

Q: Find the minimum and maximum values of the function f(x, y) = x² + y² subject to the constraint 2x +…

A:

Q: Which of the following is the correct form of the partial fraction decomposition of OA.1 + B. 1 + L…

A: The objective is to find the correct form of partial fraction decomposition.

Q: 3. fxe (4-x²) dx

A: ∫ xe4-x2dx

Q: x x +4 Give exact answers (not decimal approximations). Let f(x) = Find the values of where f'(x) =…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find three positive numbers whose product is 86 such that the sum of their squares is as small as…

A: Let the three numbers be x, y and z. x + y + z = 86 -----(1) ⇒ z = 86 - x - y ------(2) Product, P =…

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: NOTE: Refresh your page if you can't see any equations. . here we have