7. Differentiate: R(t) = tan(t) + t²tanh(t).

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A: For maximum value at a point x=a for a function f(x) is given by f'(a)=0 and f''(a)<0.

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A: We need to find area.

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A: We need to find sum of series.

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A: We know P(x)=R(x)-C(x), where P(x),R(x),C(x) are profit, revenue, cost functions respectively.

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A: Given line:y=2x+1.It is given that dxdt=4

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A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the inverse Laplace transform ƒ(t) = L−¹ {F(s)} of the function F(s) = s² = s-1 8s + 17

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Q: (i) Use the linear approximation formula or Ay≈ f'(x) Ar f(x+Ax) = f(x) + f'(z) Ar with a suitable…

A: NOTE : Since you have posted multiple questions with multiple subparts, we will provide the solution…

Q: Find the derivative of f(x) = e^m + m^x. Assume that m is a positive constant. f'(x)=?

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Q: Find the Laplace transform F(s) = L {f(t)} of the function f(t) = (9 − t) (u2(t) — u6(t))

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Q: a) Find lim √2x+3-√3x+2 x²-6x+7 b) Let f(x) = 1 2²-1 x-1' √x-1 0<x< 1 1<x<3 2-1 ' 5+3, 3< x Find…

A: Solve the limit

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Q: Use the Second Derivative Test to find the location of all local extrema in the interval (-6, 5) for…

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Q: Find dy for y = 5 sin dy= =dx 7x8 8

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Q: Consider the double integral L = 1+2²³ + y² dy dz. (a) Sketch the region of integration for the…

A: Let's sketch the graph and evaluate double integral.

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Q: 5. Solve as a linear first-order differential equation: y - 2y = x² +5

A: Solution of linear differential equation y'+P(x)y=Q(x) is given by y×IF=∫(Q×IF) dx+C, where IF=e∫Pdx

Q: 4s + 1 s³ - 3s² + 3s 1 a. Find the partial fraction decomposition of F(s): Consider the function…

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A: formula for volume is v=∫abπy2dxgiven  y=f(x)=6x for y axis x=0  a=0 and b=6

Q: Find the general solution of each of the following homogeneous equations. Use the method of…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: For the function f(x) given below, evaluate lim ƒ(x) and lim_ f(x). X→∞0 X-8 Sorry, that's…

A: NOTE: Refresh your page if you can't see any equations. . the given function is

Q: 9. Find the value of a so that the function g(x) is continuous at x = 0 where g(x) = { = 1 2xe3x 1…

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Q: Compute the line integral of the scalar function f(x, y, z) = 2x² + 8z over the curve c(t) = (et,…

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Q: Consider the differential equation -4y"" + 5y" - 5y' - 3y=0 with y(0) = -3, y'(0) = 3, y" (0) = 2.…

A: Consider the differential equation, -4y'''+5y''-5y'-3y=0 with  y0=-3, y'0=3, y''0=2. By taking the…

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A: GivenThe radius of the sphere is increasing at a constant rate of 3cm/sec.   We need to find the…

Q: Find the indefinite integral [9x (7-x¯5) dx. 9x (7-x¯5) dx = [

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Q: Consider the periodic function f(t) defined as follows: Sketch a graph of f(t) over several periods…

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Q: Which of the (i) F(x, y) = (10xy+6) i + (9xy+8) j (ii) F(x, y) = (9ye⁹x + cos 6y)i + (x + 6x sin 6y)…

A: We can find whether the field is conservative .

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Q: -, tanp Given cosa == == 12 and a and B are not in Quadrant II. Evaluate the following.

A: given α and β in 2 quadrant in 2 quadrant sinβis positive and cosβ is negative   cos(180-β)=-cosβ…

Q: -1 0 1 2 If (x)sin(2y) = (y) cos(2x), then what is dx at the point

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Q: Math questions

A: 1) Given f(x)=(2x)2 Put n=-4f(-4)=2×(-4)2f(-4)=-82f(-4)=64

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Q: Suppose that a company wishes to predict sales volume based on the amount of advertising…

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Q: 2 Identify the definite integral that represents the arc length of the curve y = 1/x over the…

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