= { x + 15 X C(x) = if x < 100 if x ≥ 100

Q: Solve (y³ + 2y² +9y+18) dx = (5x²y² x²y + 17x²) dy

A: integration using partial fraction

Q: Use a system of linear equations with two variables and two equations to solve. A number is 8 more…

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Q: A stone is thrown straight up from the edge of a roof, 925 feet above the ground, at a speed of 16…

A: solution of part A So the stone is 829 feet high 3 second later.

Q: y 3 2 1 -1 -2 -3 -4 1 2 3 4 5 6 X

A: We can find the Domain and Range of the function.

Q: (2y + √y sin x) dx + xdy = 0

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Q: y(x tan x + In y) dx + tan x dy = 0.

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Q: Calculate each of the following given that: a. b. a-b a x (2b - 3c) |b x 3c| C. d. projac a = 2i -…

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Q: Which of the following represents a possible equation for a sinusoidal function with an amplitude of…

A: answer is in next step. please give a like!!

Q: 4. Solve the following equation by completing the square. Be sure to show all steps. (round answers…

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Q: Which one of these is a vector equation for a line in 2-space? y = 3x + 7 =(-2, 1,0) + s(-4, 2, 1) +…

A: Given ○y=3x+7○r→=-2, 1, 0+s-4, 2, 1+t1, -1, 2 s,t∈R○3x+4y+7=0○r→=2, 1+t-1, 3 t∈R

Q: What is the max area of a rectangle placed between the x-axis and the function f(x)= -x^4 + 3

A: To determine the maximum area of a rectangle placed between the x‐axis and the function fx=-x4+3.

Q: What is the equation of the tangent line to y=−2x^3−x^2+4x+3 at x=3? Write the tangent line in…

A: We have to find the equation of tangent line.

Q: The following table shows the rate of water flow (in L/min) through a dam. 1 5 9 13 17 21 25 t (min)…

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Q: Find the limit of s(n) as no - + [n(n+¹)] s(n) Submit Answer

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Q: Express a = the limit lim Σ(4(x*)² – 3(x* )³) Aï; over [6, 7] as an integral. n→∞ i=1 Provide a, b…

A: The given limit limn→∞∑i=1∞4xi*2-3xi*3∆xi over the interval 6,7

Q: 1. (x³ + xy²)y' = y³ Ssangen job10 2. (2x + y)dx= xdy 3. x³y' + x²y-y²= 2x4

A: Topic:- differential equation     Definition:- The order of a differential equation is defined to be…

Q: or the equation, find the slope m and y-intercept (0, b) (when they exist). (If an answer does not…

A: An equation of the form y=mx+c called slope intercept form of line where slope = m and y-intercept =…

Q: Test Σ n 1 2" n! for convergence

A:

Q: Determine the general solution of each of the following equations: (a) y" + 2y' + 5y = 3sin2x

A: a) Given:         y''+2y'+5y=3sin2x         5yx+2ddxyx+d2dx2yx=3sin2x This differential equation has…

Q: 3. a) Examine if the following limit exists, x + y + 1 lim (x,y) (0,0) In(x2 + y²)* If the limit…

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Q: Find the equation of the tangent line to f(x) = 4x² -5x+2 at (-1,11).

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Q: The area of the région bounded by the curves f(x) = x² + 1 and g(x) = 2x + 1 is best described by:…

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Q: The graph below is the function f(x) Find lim Find lim I→-1- Find lim 4 3 I→-1+ in 2 01 I-1 es 1 2…

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Q: Exercise. Find the curvature and the radius of curvature at any point. 2. R(t) = e²¹i + (t²-1)j 90#-…

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Q: The volume of a right circular cone of radius x and height y is given by V = volume of the cone is…

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Q: Find the slope of the tangent line to the curve 2x² 4xy + 4y³ = 10 at the point ( − 1, 1).

A: SOLUTION-

Q: the interval that f(c) = k. there exists a value c, where <C Must there exist a value of c in the…

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Q: Solve the differential equation v(x) = dy dx 3y x > 0.

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Q: The position function of an object is given by r(t) = (t2, 8t, t²- 28t). At what time is the speed a…

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Q: 2) The region in the first quadrant bounded by y = x y = 2. Calculate the volume using the shell's…

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Q: = Approximate the area under the curve y = x² from x with 6 subdivisions. 3 to 6 using a Right…

A: We have to approximate the area under the curve using Right Endpoint Approximation.

Q: Find F as a function of x and evaluate it at x = 0, x = 7/4, and x = 7/2. 1-² sin € F(x) = F(0) =…

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Q: Solve the following initial value problem for the unknown function y(x) a) y' = 2xy², y(1) == b) 2…

A: Topic:- application of integration

Q: 8 Sex dx Calculate

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Q: X 2 Find x² +1 -dx

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Q: egrate the following by hand, shc 9 (a) 3 3 √x³ - 24+8) dx

A: We can solve this as follows:

Q: 4. [2 marks]. Solve the following system of equations using the Gauss-Jordan elimination method: -2x…

A: If you don't understand any step please comment.

Q: For the function f(x) shown below, determine lim f(x). f(x) = x² - 10 -3 - 2x for for +-←æ x -4

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Q: R If is in standard position and ≤0≤ and sin 2 O 5 O_3 3 3 9 then the value of tan is:

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Q: Question 13 (1 point) ✓ Saved Which of the following CANNOT be an acceptable direction vector for…

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Q: if / 2³3 rsin rda -x³ cos x + 3x² sin x + 6x cos x Oxsin x O cos x sin x X COS X = 6 ƒ ƒ(x)dx, then…

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Q: Find the area under the curve y 7 x over the interval [1, 5]

A: Given curve y=7x

Q: dy 18. x dx (1 + x)y = xy²

A:

Q: 4) Differentiate each of the following: a) y = - cos²x c) f(0) = sin(20 — π) e) y = (52)²x g) y =…

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Q: Given an, if limn→∞o an = 0 then the series 1 ∞ O diverges O converges O inconclusive O None of the…

A: series

Q: Calculate: fx²e³dx

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Q: A force of 750 lbs stretches a spring 3 inches from its natural length of 15 inches. The work done…

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Q: dy Find in each of the following: (be sure to use proper notation and simplify) dx (a) (b) y = sin¹…

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Q: Consider the function f(x) x² + 7x + 12 2-5 a. Find the first derivative. f'(x) = b. List any…

A: Solution is here

Q: 1 1 X

A: