Definition: The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles A = lim Rn lim [f(æ1)Aæ + f(x2)Ax + · · · + f(æn)Aæ]. %3D n>00 (a) Use the above definition to determine which of the following expressions represents the area under the graph of f(x) = x from x = 0 to a = 1. 1 OA. lim n00 i=1 n В. lim n00 n i=1 C. lim n00 i=1 D. lim n00 =1

Q: Given  h(r) = 1 r+3    find the following. (a) h(0)=   (b) h(−2)=   (c) h(−4)=   (d) h(x2)=       (e...

A: Answer:  The following values of H(r) are shown below as:  

Q: 8u F(u,v,w) = v+ 7w 8 Fu = v+ 7w

A: See the details solution in below

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A: We use given property and solve it.

Q: 3.4 Find the first partial derivatives of f(x, y) = 7x°y* + 9x y° +3. df = 21x y" + 18xy dx of %3D д...

A: solution

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Q: 9. 10 Consider the function f(x) x2 Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) ...

A: To find the anti derivative of f(x). 

Q: 1. Find the differential equation of straight lines with slope and y-intercept are equal. Obtain the...

A: As per our guidelines we are only supposed to solve first three parts of multiple questions

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Q: Approximate the area under the curve f (x) = x + x² over the interval [0,4] with n subintervals.

A: Approximate the area under the curve f(x)=x+x^2 over the interval[0,4]

Q: na and Minima: Problem 13 Previous Problem Problem List Next Problem Find the absolute maximum and m...

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Q: 7. Find: t2 (a) / V1+ t3 (x2 + 2)(x – 3) dx (b) / * /. - 2.x (c) xV (16 – x4 dx

A: To evaluate.a ∫01 t21+t3 dtb ∫x2+2x-32x  dxc ∫-22 x16-x4 dx    

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A: We have to choose the correct answer from the given options according to the given information

Q: If * x=t -1, y = +t, find y"

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Q: What is the value of C

A: Given; f(x) = 7x3+3x2-x+C.

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A: we will find the integration of one loop of rose curve and multiply it by 3, since all three loops h...

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Q: Provide a, o and J( x) the expression f(x) a

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Q: (a) Find F(x) = (2 - x/3) dx . (Use C for the constant of integration.) !! 3 ). F(x) = 2x – + C x - ...

A: Please see the below picture for detailed solution. 

Q: Consider the function. g(x) = 2x4 - 5x3 + 13x – 4 %3D Find g'(x). g'(x) = Find g"(x). g"(x) = Find g...

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Q: Integrate.  integral of x+2/sqrt (4-x^2)

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A: solution

Q: Evaluate the integral. 5 dx 1- 2x 0. Inl-1 + 2x | + C O -5 Inl-1 + 2x | + c O-2 In|1-2x| +C O Inl-1 ...

A: In this question we have to find the Integration.

Q: Given S(1) = / -1+ cos"(2) t „2 x + 15x + 50 f(t dæ At what value of t does the local max of f(t) oc...

A: Given information:-

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Q: (c) An open aquarium with rectangular sides and bottom is to hold 13.5 liters. Find its dimension so...

A: The solution of the problem is given in the next step.

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A: topic - application of derivatives

Q: If f (5f(x) + 2) dx = 4, then Si f(æ)dx =

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Q: . Find the slope of the line tangent to the parametric curve x = 2cost and y = 2- cos²t for 0<t<n at...

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Q: Given t2 – 1 - f(x) = dt 1+ cos?(t) At what value of x does the local max of f(x) occur?

A: Given that      f(x) = ∫0x[(t2-1)/1+cos2(t)]dt  Here we have to find at which value of x does the lo...

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A: Given:         Tangent line to the parabola                y2=6x-3  differentiating on both sides   ...

Q: (a) Find F(x) = e dx . (Use C for the constant of integration.) F(x) = x 6 In x+ C %3D (b) Find F(10...

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Q: Find the domain of * y = V2x +12 ?

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