Sketch the curve of the following:  y = x + cosx *please use handwriting not typing, I understand it better that way*

Q: If lim f(x) exists, then f is differentiable at x=c. X-C True False

A: We have given  limx→cfx exists. If limit exist then function is continuous at x=c. fc-=fc+=fc So,…

Q: 3) a) b) Suppose N(t) = (3067) (1.1) shows the number of inquiries received by the Undergraduate…

A: Given :- Nt=30671.1t Nt=Number of inquiries received by undergraduate office of a certain college…

Q: g'(x) h'(x) (or the one sided limit, as required): 5. In each case, find g'(x) and h'(x), then find…

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Q: Question 3 implicit differentiation to find the equation of the tangent line to the curve zy³ + xy =…

A: Given query is to find the equation of the tangent line.

Q: 2) d) Differentiate each function below. Be sure to use proper notation to distinguish between a…

A: To differentiate the function given below.pr=r2 tanr3r+1

Q: Consider the equation y = 3.42e-0.0096t, which is of the form y = Aert, to fill in the following…

A: The Answer is in step2.

Q: Which theorems do Kepler's Triangle relate each other with? Euler's Number Euclidian Geometry Golden…

A: Kepler's Triangle:   A Kepler triangle is a right triangle formed by three squares with areas in…

Q: e)- Assume that now X = R. Show That X. X=0 [Hint: Differentiate Constion't ev]. Deduce that I is a…

A: given: |X|=R so, X2=R2

Q: What is the symmetric difference of two joint sets equivalent to? complement of the set intersection…

A: Solution is given below:

Q: x + y - 4 (x,y)-(2,2) √√x+y-2 lim O Ninguna de las anteriores 00 04 O-4

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Q: 1. 32x+32 = 9x+1

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Q: Use the first derivative test to find the location of all local extrema in the interval (0, 2) for…

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Q: A commercial cherry grower estimates from past records that is 21 trees are planted per acre, then…

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Q: Find x and y: 1. You have 400ft of fencing to construct a rectangular pen for cattle. Then, the…

A: Topic - Application of derivatives We are given length of fencing available =400ft Perimeter of…

Q: Calculate / cot cot³(x) csc³(x) dx. Your answer should be in terms of x.

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Q: Use integration by parts to evaluate the following integral. 1 12 S 0 x In 12x dx

A: To evaluate the given integral

Q: Given f(x) = √√x+2 and 2 g(x) = x²-3x

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Q: Which of the following is the integrating factor of the given linear DE ? dy -8cos(2x) + 6ycos(3x) =…

A: Find the integrating factor

Q: Consider the graph of f'(x) given below. At what value(s) of x does f(x) have a local minimum? If…

A: Topic - Local minimum of a function. Local minimum of a function: from f'(x) ,we can find local…

Q: Use spherical coordinates. •JJJ* Evaluate te+² y² + z² dv, where E is the portion of the unit ball…

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Q: Determine all real roots of x4 +0.9x³-2.3x²+3.6x-25.2=0

A: We need to find all the real roots of :

Q: If f(x) = 3, then f'(x) = A B (c) G (3-¹) In3(3) 3*X In 3 3x

A: See the details solution in below

Q: Which of the following is a proper substitution for the following Bernoulli's equation 3 e-3x y 2x³y…

A: We have to find the substitution for the given Bernoulli's equation.

Q: For the function 1-cos.x 1-cosy + -=C, where C is a real constant, which of the following is equal…

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Q: Using a proper substitution, Bernoulli's equation dy - 5 xy = - 4 x²y4 dx will be reduced to the…

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Q: dy Use implicit differentiation to determine given the equation xy + x¹ = y². dx dy dx ||

A: Given xy+x4=y2

Q: Calculate the double integral. x sec²(y) dA, = {(x, y) 10 ≤x≤ 2,0 ≤ y ≤ }

A:

Q: 1) f(x)=ln(x^5 +x^2) f'(x)=   2) f(x) = 8sin(x^4e^3x)

A: Given functions :- 1) fx=lnx5+x2 2) fx=8sinx4e3x

Q: You have 72 feet of wire to enclose two pens. One side is a wall that needs no fence. The outside…

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Q: Make a sign diagram for the derivative of the function f(x) = x3 - 3x2 -24x+7 including all open…

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Q: The standard form of the linear DE dy 4- = 12cos(x) - 16x²y dx is

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Q: Calculate the test-statistic, t with the following information. n₁ = 45, x1 = 2.52, s₁ = 0.57 n2 =…

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Q: = The region bounded by f(x) = 2x² + 10x + 28, x = about the y-axis. Find the volume of the solid of…

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Q: If f(x) = x²√√3x+1, then f'(x) A B с D -9.x² + 4x 2√√3x+1 15x² + 4x 2√√3x + 1 9x² + 2x 3x+1 -3.x² -…

A: To find f'(x)

Q: landscape architect plans to enclose a 1000 square foot rectangular region in a botanical garden.…

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Q: 2) c) Differentiate each function below. Be sure to use proper notation to distinguish between a…

A: We will find the required derivative.

Q: 2. log6 (3x + 7) = 1 - log6x

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Q: F(x), which of the following is equal to it f(x) == F(x), dx -F(secx)? dx

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Q: if x ≤ 0 if 0 2 Use the definition for g to evaluate the following. Show work where appropriate. 1,…

A: Topic - Limits We are given, g(x)=1if x≤0(x-2)(x-1)if  0<x≤23-xif x>2

Q: Consider the following function. f(x) = x³ - 9x² + 27x + 8 (a) Make a sign diagram for the first…

A: Need to write down sign diagram of first derivative then need to find out the second derivative.

Q: Suppose C(*) represents the amount of dollars spent every miles travelled. What unit does C'(12)…

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Q: 15348 + A4CF16 = 10

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Q: 2) You deposit $100 every month in an account paying 1% annual rate compounded monthly. How much…

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Q: Rewrite the following equation in logarithmic form using the natural logarithm (ln). e¹ = c || help…

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Q: Use your derivative rules to find the derivative of the following functions: 1. f(x) = x¹ cos(x)…

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Q: Using a proper substitution, Bernoulli's equation dy - - 5 xy = - 4x²y4 dx will be reduced to the…

A:

Q: Use implicit differentiation to find y' for the equation below and then evaluate y' at the indicated…

A: Given y2 + 4y + 3x = 0point - ( -4 , 2 )

Q: lim In (x) In XX x+1 2 x+1

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Q: = 1 y' + ²y = ∙y' + a) Is the given differential equation nonlinear? Is it a Bernoulli's equation?…

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Q: 3) a) Suppose N(t) = (3067) (1.1) shows the number of inquiries received by the Undergraduate Office…

A: Topic - Application of derivatives We are given, 3.)N(t)=3067(1.1)t Where N(t) is the number of…