Approximate S“ In x dx using three rectangles of equal length and left end points. Is your estimate an over or under estimate? How can you tell?

Q: The surface area of a sphere, initially zero, increases uniformly at the rate of 4 xq.in. per sec…

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Q: The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the…

A: The radius of the sphere is increasing at a rate of 5mm/sits diameter is 80 mm

Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the…

A: Write the expression for the volume of the sphere and take the derivative then substitute the given…

Q: Use Simpson's rule with interval h = 1 to determine the approximate value of 6 V(1 + x³)dx. Give…

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Q: 2. The radius R of a circle is increasing at the rate of 1cm per sec. how fast is the area changing…

A: To find: The rate of change of area when . Formula used: Area of circle having radius R.…

Q: Estimate | (2x – 5) dx using left endpoints for n = 3 approximating rectangles. %3D 5 (2x – 5) dx is…

A: Given: ∫152x-5ddx The left Riemann sum (also known as the left endpoint approximation) uses the left…

Q: Describe the change in accuracy of dz as an approximation of ∆z as ∆x and ∆y increase.

A: Given , z=fx,yWe do dz using the partial derivates zx & zy .So , dz=zx.dx & zy.dywhere zx…

Q: The surface area of a sphere of radius r is A = 4r?. If the surface area is increasing at a rate of…

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Q: Estimate (2x – 5) dx using right endpoints for n = 3 approximating rectangles. (2x – 5) dx is…

A: We have to estimate the , ∫15(2x-5)dx using right end points for n=3

Q: Calculate an approximate value of the integral ; dx by dividing the 1+x2 interval into 8 equal parts…

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Q: ind the rate of change to total revenue (in dollars) with respect to time when x = 10 and given that…

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Q: Find the indicated derivative and simplify. Int dy for y = dt et dt

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Q: (a) Determine the interval width so that the composite trapezoidal rule can be used to compute xe*dx…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: The approximated value of the integral fe* dx is equal to - Rule with step size (h=2). when using…

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Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the…

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Q: Find the most general antiderivative or indefinite integral. dx

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Q: and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this mom

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Q: The radius R of a circle is increasing at the rate of 1 cm per sec. How fast is the area changing…

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Q: Two students are calculating the instantaneous rate of change of y= sin(x) at x = Student A claims…

A: Given is the function y=sinx and the point is x=π3 The rate of change is represented by two students…

Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in…

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Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

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Q: Use Simpson's rule with interval h = 1 to determine the approximate value of f V(1+ x3)dx. Give…

A: Given integral is ∫021+x3dx and h=1. We have to approximate the given integral by using Simpson's…

Q: Assume a circle is expanding with time, where r = t + 2. What is the formula for the rate of change…

A: Given: r = t + 2   We know that the area of the circle: A = π r2   where r is radius.

Q: Use the Midpoint Rule with n = 4 to approximate 2x the integral 1 dx to three decimal place.

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Q: At what rate is the area of rectangle changes if sides are x and 4x, if the shorter side x changes…

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Q: Find the approximate value of f 10. ' to 4 decimal places using e su

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Q: Use the Simpson's rule to estimate S, ex dx with n = 4

A: Consider the given integral ∫12ex2dx with n = 4. Simpson's rule is,…

Q: If the area of a healing wound changes at a rate given approximately by dA 4 for 1 <t<10 is in days…

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Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

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Q: Use integration by parts to prove the reductionformula.

A: We have to prove the reduction formula using integration by parts method: ∫xnexdx=xnex-n∫xn-1exdx If…

Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

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Q: The area under the curve y = cos x from x = a to x = is 0.2. What is the value of a 2 rounded to…

A: Area under a curve y(x) is given by ∫abydx         where a≤x≤b

Q: Write your own definite integral where the total area under the curve is 20.

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Q: 15. Use the table of integralsto evaleuate, the integral. ex dx

A: We have to evaluate the integral ∫ex1-e2x32dx by using the table of integrals.

Q: ce of a circle is increasing at a rate of 2 cm/s. rea increasing when r= 6 cm?

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

Q: MY N nd the minimum value of n that guarantees an error of no more than 1/30,000 in approximating -…

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Q: The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the…

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Q: Estimate (2x – 5) dx using midpoints for n = 3 approximating rectangles. (2x – 5) dx is…

A: 4

Q: Use Simpson's rule with interval h = 1 to determine the approximate value of V(1 + x³ )dx. Give…

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Q: Use the differential dV to estimate the change in volume of a cube when the side length changes from…

A: We need to use the formula for differential to estimate the change in volume when side of the cube…

Q: The area of a rectangle with one of its sides s is A(s) = 6s². What is the rate of change of the…

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Q: Use the Simpson's rule to estimate e**dx with n = 4

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Q: The area A(t) of a circular shape is growing at a constant rate. If the area increases from 97 to…

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Q: 7) Estimate the value of e dx using Simpson's rule using 8 subintervals.

A: Given: ∫02ex2dx Here, n = 8 subintervals

Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A: Consider a function y= f(x)  then the derivative f '( x) is the  rate of change of y with respect to…

Q: With n > 0, does x" dx get larger or smaller as n increases? Explain graphically.

A: Given: The given integral is ∫01xndx. Calculation: Use the integral formula, ∫xndx=xn+1n+1+C.…

Q: Use the Trapezoidal Rule with n = 4 to estimate f, x² dx. Compare the estimate with the exact value.

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Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: Consider the given equation. dndt=4t+1 first find the solution of the equation.…