2.

Q: Evaluate the following limit. : - lim 5-2 メタ8 イー&

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Q: Let f(x) = |x| +3, x s 0. a) Draw a graph of f(x). b) Explain why f(x) is one to one. c) Find f-1(x)...

A: Here we have given function isy=|x|+3

Q: Write the composite function in the form f(g(x)). [Identify the inner function u g(x) and the outer ...

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Q: If J_f{x)dx=10 andJ, f{x)dx= 3, then J, f(4 – x)dx=?

A: According to our guidelines we are supposed to do only one question. Kindly repost the other questio...

Q: 1 1 + 25 1 Consider the geometric series 1+ 1 + .. 125 625 This series can be written in the form ar...

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Q: 10 If f is a continuous function and F'(x)=f(x) for all x€ R, then J x=? O IFS) - F)] 2[F(5) – F(1)]...

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Q: Solve the DE f'(x) = 5x given that f(0) = 3. %3D A y +3

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Q: A certain slug is fired and its position is described by the following equation in x and y direction...

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Q: Perform the test of exactness in the given DE. What will be the value their partial derivatives * (e...

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Q: dy -=2x – 3 and y=2 when x=3 what is the value of y when *=6? dr Suppose Write the answer in its exa...

A: Given: dydx=2x-3y=2, when x=3 To Find: To find the value of y when x=6.  

Q: The region W is the cone shown below. The angle at the vertex is 1/3, and the top is flat and at a h...

A: Angle at the vertex = π3 Height of cone = 83

Q: The definite integral . °lcot?(x) + csc²(x)]dx when evaluated is equal to AV 3+ Br where A, B are co...

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Q: Determine the derivative of the function defined by h(x, y) = Arctan () + v3Arcsin () %3D at the poi...

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Q: IfI represents the intensity of light which has penetrated water to a depth of x feet, then the rate...

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Q: dy Suppose =ky, where k is constant and y=8 when t=0. Also suppose that y=6 when t=3. what is the co...

A: We have to find value of k by given information.

Q: Consider the following position function. Find (a) the velocity and the speed of the object and (b) ...

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Q: 2x dx = x² + 2x+1 1 +C x+1 A arctan x+ 2 B 2ln|x+1| - +C (x+1)2 1 +C x+1 -arc cot x 2 +C x+1 2ln|x+1...

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Q: F (6) = S+5)° Co

A: The given function is: F(s)=s(s+5)9⇒F(s)=s+5-5(s+5)9⇒F(s)=s+5(s+5)9-5(s+5)9⇒F(s)=1(s+5)8-5(s+5)9

Q: Suppose f(x) =- . Evaluate: 3x+4 Write the answer in its exact form as an integer of a fraction in l...

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Q: dy = 4cos(2x) and y=2 when *= 3x Suppose What is the particular solution to the given differential e...

A: Let's find. 

Q: The population of a country is growing at a rate proportional to its population. If the growth rate ...

A: Let population at time  t is given by  P(t)

Q: Given x = 2 cost + 10 and y= 8 sin? t dx (i) dt dy (ii) dt dy (iii) dx

A: Let's find. 

Q: Given the periodic function f(x)= x|x| over the period [-1/2, n/2]: a. Plot fx) on the interval [-7,...

A: As per our guidelines we are supposed to solve only first three subparts of the problem. For those f...

Q: 7. 5'15' 15' ...

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Q: Find the mass of the lamina described by the inequalities, given that its density is p(x, y) = xy. (...

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Q: 5. (4xy + 3y² – x)dx + x(x + 2y)dy = 0

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Q: Find the particular solution of the differential equation (xcosy + cos?y)dx = 2x²sinydy = 0 when x =...

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Q: Use the Change of Variables Formula to evaluate the definite integral. cos* (x) sin(x) dx (Use symbo...

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Q: The population of a country is growing at a rate proportional to its population. If the growth rate ...

A: Given ,  The population of a country is growing at a rate proportional to its population If the grow...

Q: k+3 If fx+ k)dx=8, where k is constant, f(x+ J (x)dx=? then k-1

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Q: II. Integrating Factor by Solution. Solve the following differential equations 4. y(4x + y)dc – 2(x²...

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Q: Determine the linearity and solve for the general solution to the given DE dx = ecos y dy х cot y

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Q: Evaluate the limit using L'Hospital's rule 15* – 12" - lim

A: We have to find limit

Q: Va+x-Va (c) 1 is 2va Prove that the lim x→0 a + bx, for x > 2 3, for x = 2 b — ах?, for x < 2 (d) Co...

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Q: A colony of bacteria is growing in a petri dish which has a maximum capacity of 140mg. The mass of b...

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Q: dy Suppose =ky, where k is constant and y=6 when t=0. Also suppose that y=8 when t=3. what is the co...

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Q: Among the given choices, which of the following definite integrals have the largest value? A dr B x2...

A: We need to find the largest value from the given definite integral. This can be done as follows:

Q: Suppose f (x) = 3*sec(3*) tan( 3*). Evaluate: sec(3*) +C In (3) A 3*. sec(3*). +C In (3) © In (3) - ...

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Q: |vxa| Use the alternative curvature formula K= to find the curvature of the following parameterized ...

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Q: The function y = f(x) is given by the figure. 2 y = f(x) 1 1 3 4 5 6 -1 Find the minimum and maximum...

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Q: .Is f (x) = x sinx a periodic function ? %3D

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Q: Solve the equation (4ху + Зу? — х)ӑx + x(х + 2у)dy — 0. а. 4ху+ 4y? — х — с с. х?(4ху — 4y? — х)— с ...

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Q: Question 4 Let f(x) = |x| + 3, x < 0. a) Draw a graph of f(x). b) Explain why f(x) is one to one. c)...

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Q: 5 Suppose f(x)= )dr AV 4x-3 +C, for constants A and C, what is the value of A? 4x -3 Write the answe...

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Q: Consider the function below. f(x) = 6xtan(x), -n/2 < x < n/2 (a) Find the interval where the functio...

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Q: 3. A lot in rectangular shape is to be fenced off along a highway. The cost of the fence on the high...

A: We have to find largest area

Q: smallest values of the function f(x, y) over the given boundary critical points and determine the la...

A: Given fx,y=xy-x-3y

Q: Sketch the graph of the following. Find the values of a, b, period, phase (if any) and vertical (if ...

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Q: .3 If U = 2 – x, | x/2- xdx= = n} .3 -J uvūdu В (2 – u)/ūdu | .3 © (2- u)/ūdu 1 (D uvūdu A)

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Q: in the same Cartesian plane, sketch one cycle of the graphs of y = 3 sin sin x and y = 3 sin sin (x ...

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