What is the limo+ (√In(x))? For answers that are fractions infinity ti infinitu write... in decimal form and round off to two decimal places 999999 000000 /

Q: (a) Find the average rate of change of f(x) from x = 1 to x = 2. 7 (b) Using the definition of the…

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Q: Find an explicit solution of the given initial-value problem. dx = · 3(x² +1), x(7) = 1 dt X =

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Q: Evaluate the following integrals. y = f(x) a. b. C. d. 16 0 f(x) dx [f(x) dx Ja (2|f(x) +3f(x) dx…

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Q: Solve linear diff eq dy/dx = e^(-x) -4y ; y(0)=-10

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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: h(t) = + 3²²-t t

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Q: 2|6x + 4 ≥ 1 OX - 7/12 O-7/12 - 12/7

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

A: Just I have used the method of exact differential equation and then solved it .Final  solution is in…

Q: lim[1-sin x] 19. 0 3 lim(1 + sin x) 20. x→0

A: 19) limx-0[1-sinx]1/x 20) limx-0[1+sinx]3/x.

Q: 8) y(y³- x) dx + улу x(y² + x) dy = 0

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Q: If the equal tensions T in the pulley cable are 520 N, express in vector notation the force R…

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Q: Find the volume of the given solid. Under the plane 3x + 2y - z = 0 and above the region enclosed by…

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

A: Let's evaluate given integral.

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: If the tangent line to y = f (x) at ( 5, 3) passes through the point (1, - 2), find f' (5)=

A: Given problem:- If the tangent line to y = f (x) at ( 5, 3) passes through the point (1, - 2) Find…

Q: dy If x³+y³ = 1, what is -? dx² D OC O 22(23 ys 2x(2 − y) y³ 2x y5

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Q: Given: f(x, y) = 3xey - 2ye-x Find: 0² f(x,y) Әх у 0 3x - 2e"* 0 Зе" + 2e-* 0 3e 0 3x + 2e-*

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Q: Find u · (v ✕ w).

A: Here we have to find the given vector operation

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 a vector function (a) Find the domain of r(t). (b) Find the limit lim r(t). t→1 (c) Find the…

A: The objective is to solve the above question.

Q: Use the Factor Theorem to determine whether x+1 is a factor of P(x)= 2x4 +2x3 -6x2 +6…

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Q: X1 + 4 x2 + 3x3 = 2 2x16 x2 + 6x3 = -3 5x12x2 + 3x3 = -5

A: Given :2x1+4x2+3x3=22x1-6x2+6x3=-35x1-2x2+3x3=-5

Q: If t = 12, then Y12 = 4, 727, 272e (In 1.17 10 12 5,707, 340

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Q: d) y = 21+1 31-2

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Q: Solve the given initial-value problem. x(x + 1) dy + xy = 1, y(e) = 1 dx y(x) = Give the largest…

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Q: What is the lim→( For answers that are fractions infinity negative infinity 7 sec (7x) cos(3x)?…

A: See the details solution in below

Q: Use the Limit Definition of the Derivative to find f'(x) for the following function. You may NOT use…

A: Using the limit definition of the derivative

Q: 9. Find the volume of the solid generated by revolving about the y-axis the region bounded by the…

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Q: Find all the local maxima, local minima, and saddle points of the function f(x,y) = x² + xy + y² +…

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Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: Given: f(x, y) = ln[1 + x siny] Find: 8² f(x,y) 8x² 2 sin y (1+xsin y)² ○ _ __ sin² y (1+zsin y)²…

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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: 3. find the derivative 513.5+412.52¹.7 lt Enter your answer

A: Taking derivative of the function with respect to t and using power rule of derivative gives the…

Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity (feet/second) t…

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Q: C. 1-3/5 (6x³+11x² - 4x) 18x² +22x-4) dx

A: We can solve this as follows:

Q: Find the area of the region bounded above by y = x + 2 and below by y => X 542 1 1 2 3 4 5 -2 -3 O O…

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Q: = 2. If y = sin³ (-) cos³ (1) prove that y' = sin² (x) cos(x)

A: Topic = Derivative

Q: Q1: Find the general solution of the following first order D.Es a) (xy² + x)dbe+(a + y)dy =…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 1) lim (tan x) cos x X-2

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: A farmer plans to enclose a 200 ft^2 rectangular field that borders a straight river. He needs no…

A: The solution is given in the next steps.

Q: dy/dx=x-4xy Solve using integrating factor and seperating the variables

A: Topic = Differential equation

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: 4. Find the area of the region enclosed by x = 2y+3 and x = y².

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

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Q: Evaluate the line integral F(x, y, z) = (x,-z, y). Jo F. dr where C is given by r(t) = (2t, 3t,…

A: We will use concept of parameterization to solve this.

Q: A species of bacteria has a population of 250 at 6 a.m. It doubles every 8 h. a) Determine the…

A: Given: Population at 6 a.m =250

Q: By L'Hopital's Rule, X-2 lim x→2 X²-1 1 1 lim. = x→2 2X 4

A: L’Hospital’s Rule: Suppose that  limx→a f(x)g(x)=00  OR  limx→a f(x)g(x)=±∞±∞ where a can be any…

Q: Find an explicit solution of the given initial-value problem. (1 + x4) dy + x(1 + 4y2) dx = 0, y(1)…

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Q: Determine whether the statement is true or false. fy(a, b)= lim f(a, y) - f(a, b) (y - b) O True O…

A: Given fy(a,b)=limy→bf(a,y)-f(a,b)(y-b)