Evaluate the given limit. Show your complete solution. limx→∞ [e5z + x²]

Q: Suppose two positive real numbers a and b add to 120. Find the values of a and b that maximize the…

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Q: Let f denote the function if x < 2; 1 f(x) = if x 2. Which of the following is true about f? Of is…

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Q: Solve the differential equation. 2. (y^2-2xy + 6x) dx – (x^2 – 2xy + 2) dy = 0

A: To solve the given diffrential equation.y2-2xy+6x dx-x2-2xy+2 dy=0

Q: Given w = xex + ln(x²yz3) Determine дш дх O дш дх δω дх ди дх дш дх = ex(1 - x) + = xẻ +1+ 11 N|X 2…

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Q: c - [² x ² (1 - √x ) ³dx 0

A: In this question we have to evaluate the Integral.

Q: Problem 2. A cylindrical can without a top is to be made to have volume 100cm³. Find the radius of…

A: We have to use a concept of derivatives

Q: 2. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

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Q: Given: f(x, y) = ln[1 + x siny] Find: g² f(x,y) 8x² 2 sin y (1+xsin y)² sin² (1+2 sin y)² 1+2 sin…

A: In this question, we need to find the second partial derivative of the given function.

Q: C- - 0 x4 (1-√x)5dx

A: we  need substitution method to evaluate given integral

Q: d- dx3 ax d² y dx² +6- 15 dy dx Q.2-Solve the differential equation 100y = 0

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Q: Let f denote a piece-wise defined function whose graph on the closed interval [-3,3] is shown below:…

A: f denotes piece wise function .  Identify the interval where function is concave down

Q: What is the lim+∞0x².e-²? For answers write... that are in decimal form and round off fractions to…

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Q: Find and sketch the domain of the function. f(x, y) - In(4x2 - 4y²) y

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Q: Suppose that a product currently sells for $24, with the price increasing at the rate of $5 per…

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Q: Find the area of the region bounded above by y = x³ + 1 and below by y = x + 1. 3 2.5 2 1.5+ 3.5…

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Q: Evaluate the line integral F. dr where F(x, y, z) = x²y i+ x³ j+e² tan-¹ z k and C is the curve of…

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Q: x²-3 (x-1)² . Analyze and sketch the curve given by f(x)=- if y': 2(x-3) (x-1)³ 4(x-4) (x-1)* and…

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Q: A solid has a base in the form of an ellipse with major axis 10 and minor axis 8. Find its volume if…

A: Given that, A solid has a base in the form of an ellipse with major axis 10 and minor axis.

Q: (x + 1) dy = −y + 20 dx O separable exact linear in x linear in y O homogeneous Bernoulli in x…

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Q: The trigonometric function is defined by ƒ(x) = 2sin4(x-7)+4 a) tate the transformations and key…

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Q: Solve the following equations:السؤال الثالث حل نظام المعادلات by using Cramer's rule باستخدام طريقة…

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Q: Use synthetic division to find the quotient and remainder when 2x3 -8x2 -1 is divided by x

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Q: Find the general solution of the given differential equation. x²y + xy=5 y(x) = Give the largest…

A: To find the general solution of the given diffrential equation.x2y'+xy=5To give the largest interval…

Q: 4. Find the volume generated by revolving the area cut off from the parabola y = 4x - x² by the x…

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Q: 49-7 Estimate lim *-7 -7 is approaching to using a table of functional values.

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Q: Q2 (a) Sketch the following function of period 27. f(x)= |x| (-1 ≤ x <n) f(x + 2x) = f(x) (b)…

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Q: The revenue in dollars for a product is given by the function R(x) = 36x -0.01x² where x is the…

A: To find average rate of change in revenue as x varies.

Q: 4. Let X: +3 if x < -2 if -2<x< 1 h(x) = {x² -x+2 if x2≥1 a) Find the following limits if they…

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Q: Given: f(x, y) = arctan Find: F ƒ(x, y) dxdy x² - y² (x² + y²)² 3²-x² (x² + y²)² -y³ (y³ + xy²)² y²…

A: Given: fx, y=arctanxyTo Find: ∂2fx, y∂x∂y

Q: A skydiver weighing 176 lbf (including equipment) falls vertically downward from an altitude of 5000…

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Q: The area bounded by the parabola y2 = 4ax, its axis, and its latus rectum revolves  about the x-

A: Given: y2= 4ax

Q: x sin æ+tan² I lim, 0 1-cos

A: We can solve this as follows:

Q: In (x-2)² In sketching y determine the intersection of the curve and the horizontal asymptote. None…

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Q: y=xe

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Solve the differential equation. 8. x ( 3xy – 4y^3 + 6) dx + (x^3 – 6x^2y^2 – 1) dy = 0

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Q: Differentiate the following functions. You do not need to simplify, but you must show all your work.…

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Q: Q4: A-Evaluate: fx exdx, using Gamma function applications. B-Find the Laplace transform of: f(t)=…

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Q: 10. DETAILS ZILLDIFFEQMODAP11 3.1.023. MY NOTES ASK YOUR TEACHER A large tank is filled to capacity…

A: To find the number of At

Q: Find the area of the largest rectangle that can be inscribed in a circle of radius 20 cm. Answer:…

A: We know that maximum area of rectangle in any circle is square.

Q: The domain for the function ex y = x ln(3 - x) is {x/x 3} O

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Q: Give a general solution of the differential equation y"–9 y = −2t cos 3t

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Q: 12. DETAILS ZILLDIFFEQMODAP11 1.R.001. Fill in the blank. The symbol C₁ represents a constant. d =…

A: The solution is given below.

Q: Expand and simplify. 3(2y-3) 2(4y-1)(4+1) Factor: a. 3x² + 16x-12 b. x²-y²-6y-9

A: We will solve all 3 subparts in the following steps.

Q: lim,→-1 22²+2-1 2+1

A: See the answer below

Q: Solve the given differential equation by separation of variables. y In x dx x dx = (x + 1)² 12/2+2 =…

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Q: Find f'(a) using the definition of the derivative at a point for f(x) = 1 VI at a = 7.

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Q: Find the first partial derivatives of the function. f(r, s) = r ln(r³ +56) fr(r, s) = fs(r, s) =

A: To find out the first partial derivatives.

Q: What is f(2022) (cos x), the 2022nd derivative of f(x) = cos x? COS X sin a sina

A: To find 2022nd derivative of f(x) = cos(x).

Q: Find a general formula for f(n) f(x) = (x-2)-¹ (Use symbolic notation and fractions where needed.)…

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Q: If 2x + 3y = à and -x + 5y = 6b, express x and y in terms of à and b.

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