At what points of R² is the following function continuous? 17 f(x, y) = x5 (y² +81)

Q: Determine whether the differential equation (7x² - 2xy + 6) dx + (7y² − x² + 7) dy = 0 is exact. If…

A: The differential equation,    7x2-2xy+6dx+7y2-x2+7dy=0

Q: 1. Evaluate the improper integral 150 xe dx or state that it diverges.

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Q: dy Q:4) Solve the following differential equation: = 1+ x + xy + y

A: The solution is given below.

Q: Find the general solution of the given differential equation. xdy+3y=x²-x dx y(x) = Give the largest…

A: The objective is to solve the above question.

Q: A) Find the Laplace transform of (2 03

A: We have to solve given Questions.

Q: Find for THREE of the following functions: dx 1-y()+In(cos(x)) + √2-y=2(cos(x))*(x)

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Q: Direction cosines are calculated using: The angle between a vector and one of the coordinate axes.…

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Q: 2 ln x + ln (x+1)- 1/2ln (x^2+1). Compress the logarithmic expression.  PRE-CALCULUS HW question..…

A: The given expression,   2 lnx+lnx+1-12lnx2+1

Q: dy 2 +6y=3 dx y(x) = Give the largest interval I over which the general solution is defined. (Think…

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Q: For the following set of planes, determine which pairs of planes in the set are parallel,…

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Q: Find the equation of the plane tangent to the following surface at the given points. x² +…

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Q: find the area.  x^2=8y and x=y+1

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Q: Find an implicit and an explicit solution of the given initial-value problem. (Use x for x(t).) dx =…

A: The given initial-value problem,dxdt=4x2+1, xπ4=1

Q: a) Graph the function f(x)=2x-5x + 3. b) Draw a tangent line to the graph at the point whose…

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Q: Evaluate the following double integral over the region R by converting it to an iterated integral…

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Q: 8) S dx it sinx + cos x a) in (1 + tan =) + c b) In (i - tan £) + c c) - In (1 + tan x) + o 2 d.)…

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Q: A manufacturer's total cost equation per day is given by the equation TC = 440+4q+,00010². If each…

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Q: 1. Evalaute lim ƒ(x), lim ƒ(x), lim f(x) for I-3+ H-3- I-3 f(x) = { 2 -x+4 x - 3 x <3 I 23

A: Topic = Limits As per guidelines , At a time only one question can be answered. please repost for…

Q: What is the slope of the tangent line to the graph of the solution of y' = 7√x + 6x³ that passes…

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Q: Find an explicit solution of the given initial-value problem. +²dy x=y=xy, y(-1) = -4 dx y =

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Q: 1) a car is slowing down at the rate 0.8 ft /sec², How the will the can move before it stops if its…

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Q: Given the graph of fx), determine the range of f(x) • 8 -10-9-8-7-6-5 OR O(-1) (1.) O(-2) u (2) O(1)…

A: Range of an inverse function is the domain of the orginal function.

Q: A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.…

A: To find the maximum hight of the ball.

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

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Q: The curve y = ax² + bx+c passes through the point (3,6). The line y = 4x + 1 is tangent to the curve…

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Q: Q4\ Solve by Gaussian elimination x-4y-2z = 21 2x+y+2z = 3 3x+2y-2=-2

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Q: 0 3² 3x - 4x dx 5x

A: Basic identities of integration are used.

Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

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Q: Differentiate the function. G(x) = (x³-8). G'(x)= 2 x + 25 x²-25

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Q: 2 Heather has a bag of 15 red, 11 orange, 9 yellow, 12 green, 6 blue and 11 purple markers. How many…

A: Heather has a bag of 15 Red ,11 orange ,9 yellow ,12 green ,6 blue and 11 purple. Find how many time…

Q: 5) Find f'(x) given that f(x) = (2x³ + 2x² − 3)(3x³ − 2x² + 4)

A: In this question, we want to differentiate the given function f(x).

Q: If f(x) is linear, g(x) is linear, and h(x) = f(x)/g(x) What is the maximum number of vertical…

A: fx is linear, gx is linear and hx=fxgx

Q: 6 6 Suppose ff(x) dx = −4 and g(x) d -4 3 3 6 Evaluate (3 f(x) — 3 g(x)) dx. 3 Remember to include a…

A: Given that ∫36f(x)dx=-4   and ∫36g(x)dx=-3 we have to calculate , ∫363fx-3gxdx. To solve this…

Q: Find the solution of the given initial value problem in explicit 1 y' = (1 — 11x)y², y(0) = ——— 6…

A: We can solve the given differential equation by using the variable separable method.

Q: Find the solution of the given initial value problem. π ty' + 2y = sint, y "(-) = 5, t > 0 Y ||

A: Concept: linear differential equation of the form dydx+Py=Q The general solution of the linear…

Q: Let y = f(x), where f(x) = 5x² + 5. Find the differential of the function. dy = X

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Q: [1 if A= 2 13 23 2 1 -2 find det (A) if 3 3 -1. 6 O 38 O 16 O 18 O 48 O

A: The solution is given in the next step.

Q: Find the solution of the given initial value problem. ㅠ ty' + 2y = sint, y (-) - = 5, t > 0 Y ||

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Q: Evaluate the integral. 1 u5 1 [(4-3- du u √√2 5 1 --- 4 3 1 √2 du = (Simplify your answer.)

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Q: Find the derivative of the function. g(x) = (sech(7x))² g'(x) =

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Q: Find the volume of the solid generated by rotating the region enclosed by y = x + 3, y = 0, x = 1,…

A: Topic = Volume

Q: Find the indicated limit if it exists. √x+4-2 a) lim X-0 X 8x³+27 b) lim x-1.5 2x + 3

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Q: Solve the given differential equation by separation of variables. dp = P - p² dt et+c P = _t+c X

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Q: Q5) Solvex+2xy = 3 by using Euler's method to find he approximate solution up to X-2.9 when h = 0.5…

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Q: Consider the following. f(x) = { J-7x, X ≤ 4 1x² - 2x + 7, X > 4 Find the x-value at which f is not…

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Q: Determine whether the differential equation (4x² − 2xy + 6) dx + (2y² − x² + 4) dy = 0 is exact. If…

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Q: * The following function f(x) = x^4 sinx is odd O neither O O even

A: The given function fx=x4 sinx

Q: 0 3x - 4x 5× dx

A: We have to solve given Questions.

Q: The normal line to a curve h(x) = -x² + 1 at point Z, is defined as a line that passes through point…

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Q: Consider the following autonomous first-order differential equation. d = y In(y + 2) Find the…

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