4- A small ink-blot of area 1 cm and radius r(t) on a piece of absorbent paper spreads in time t sec into a circle where the radius of the circle increases in time as: 1+t² r(t)= 5+t² How long does it take the ink-blot to cover an area of: (a) 1.50 cm² (b) 1.75 cm² (c) 2.00 cm²

Q: If  z = 8x2 + y2  and  (x, y)  changes from  (1, 1)  to  (0.95, 0.9),  compare the values of Δz…

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Q: Evaluate the following integral by interpreting it in terms of areas from drawing the graph of the…

A: Given data

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A: Here we have to find the anti derivative i,e integration of p(t)Given p(t)=1t23or, p(t)=t-2/3

Q: 2. a. S_14x² + 2x + 1 3 X Evaluate the indefinite integrals. dx b. f(2 sec¹x + sin(2x)) dx

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Q: Use properties of integrals to determine the value of when S² se I = √₁²5 (² f(x) dx = 12, f(x) dx […

A: given→  I=∫05f(x)dxwhen  ∫07f(x)dx ,  and  ∫57f(x)dx

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Q: 28. ƒ、(2,4) if ƒ(x, y) = xª ln y

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A: We have to find the lower bound of the interval in which the roots of the polynomial lie.

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Q: Evaluate the definite integral. 4 4 12(In x)5 X 12(In x)5 X dx dx= 0 (Round to three decimal places…

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Q: 3) Consider the function g(x) = cos(3x). a. Write the first three non-zero terms of the Maclaurin…

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A: It is given that the function is fx=x2-x2x-32. It is known that if the second derivative of the…

Q: 7. Determine the indefinite integral 4x 2 x² +5° -dx

A: let  H=∫4xx2+5dxformula used→(i)  d dx(xn)=nxn-1(ii) ∫1xdx=lnx+c

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A: .

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A: Given Profit on a pair of ski pants is $2.00  and on a jacket is $1.50. There are 60 minutes of…

Q: Find f. f(x) = f'(x) = √(3 + 10x), f(1) = 11

A: Given: f'(x)=x(3+10x)f(1)=11 We are required to find: f(x)

Q: 1. Derive the expansion sin(2²) 11 -1% 22 1 22 3! + 5! 10 7! +... (0<=<∞0).

A: We shall use the expansion of sinx

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A:

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

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A: NOTE: Refresh your page if you can't see any equations. . the given constraint is  subject x2 .…

Q: 20. The parametric chain rule states dx II dy dt. Prove this statement. dx dt 21. Explain how the…

A: (20)

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A: Need to perform indicated integral. Instagral will be definite.

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Q: 1. Find the family of antiderivatives of the following functions. (a) x² + 3x -S CbDe - (+ain (8)…

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Q: Q.6 Given the functions: f (x) = x 2 - 9 and g (x) = x-3, what is (f / g) (x)?   x + 3 x - 3 x -…

A: We have given f(x) and g(x) and we have to find (f/g)(x).   According to our guidelines we can solve…

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A: Need to perform integral using substitution.

Q: Find the net signed area between the f(x) and the x-axis:

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Q: 1. Use the ratio test to determine whether the series -13 is absolutely convergent, conditionally…

A: The given series is: ∑n=1∞ en+1n 3n

Q: Question Given du = ux² where u(3) = 1, solve for u. dx Provide your answer below: u=

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A: given  S=800000e-0.2twhere S is weekly sales in dollars and t is number of weeks

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Q: Divide f(x) by d(x). Your answer should be in the following format: R(x) f(x) = Q(x) + d(x) (x) =…

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A: given  S(t)=700e0.07twhere t is the number of years

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Q: Write the rule of a function that gives the perimeter of a rectangle of length L and width w. P(L,w)…

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Q: Use substitution to find the indefinite integral. S9(9x - 8) dx [9(9x-8) dx =

A: let M=∫9(9x-8)6dx  formula of integration→(i) ∫xndx=xn+1n+1+c

Q: Given the function f(x) = 3, compute the left-endpoint (Riemann) sum using n = 4 on the interval…

A: Given functionf( x ) = 1x2 + 3n = 4 interval = [ -2 , 2 ]

Q: Find the absolute maximum and absolute minimum for f(x) = x³ — 12x + 12 on the interval [0,3].

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Suppose -1 [ f(x)dx = -6 and -1 [²9(x)dx = -4 and [ f(x) dx = 3, -1 (b) f(f(x) = g(x) dx -2 1,96…

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Q: A juice company has found that the marginal cost of producing x pints of fresh-squeezed orange juice…

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Q: 5. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. a) S…

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Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

A: ft=4t2+1t2-1

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Q: Determine the General Particular Solution of the following DES.

A: We have to find the solution of the given differential equation.