Evaluate the following definite integral. Express your answer in terms of logarithms. In 6 S In 5 cosh x 2 4 - sinh-x dx

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Q: 5. The sum of thrice a number and two equals 6 less than four times the number. Find the number.

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A: A function is continuous at x = c iff limx→c+f(x)=limx→c-f(x)=f(c)

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Q: (5) (a) For all n € N and a + 0, show that k=1 11 1 1

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A: To determine the drug usages, doctors estimate a person's body surface area BSA in meters squared…

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A: We need to find the limit limx→∞ x-12x2-7x

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A: We have to compare the values of Δz and dz.

Q: Write the following equation in logarithmic terms. Do not simplify your answer. e5 = 4.5 Answer ||…

A: we have to write the given function in logarithmic terms . For this, first we should know some…

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A: We will use concepts of translation , dilation and reflection.

Q: Consider the following function. 1 x² - 25 Complete the following table. (Round your answers to two…

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Q: Describe the transformations that map the function y=2^x on the function y=2^x+3

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A: y = x4/4  length of curve formula  = ∫a b1+(dy/dx)2 here limit given from 2 to 4  a = 2  b = 4…

Q: work. a) ( i) Find the exact length of the curve 1 <2

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Q: 1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves.…

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Q: ind the solution of the given initial value problem. y(4) 10y" + 25y" = 0; y (1) = 8+e5, y'(1) = 6…

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Q: The masses m, are located at the points P. Find the center of mass of the system. = 2, m3 4, m2 6.…

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Q: Find the interval of convergence of the power series .x" /n². 0-1<x<1 0-1<x< 1 0-1≤x≤1 O-1<x< 1

A: The given power series is xn/n2.

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Q: Estimate the slope of the graph at the points (x₁, y₁) and (x2, Y₂). At (x₁, y₁), slope At (x, y₂),…

A: We know:- sllope of a line passing through two points =y2-y1x2-x1

Q: Q7 a) (-) lim x-0 b) (₂) 2 lim 48 3r

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Q: If f(x) = 4x² - 5x + 5, find f'( − 3). Use this to find the equation of the tangent line to the…

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Q: If the region under the graph of 1 x² y = x² + from x = 1 to x then the volume of the resulting…

A: The objective of the question is determine the volume and choose the correct option.

Q: Evaluate the integral, which has irreducible quadratic factors. (Use C for the constant of…

A: We will find the integral.

Q: Evaluate the limit. 1-x² lim *+1 sin(27x) a) lim b) x+2x² C) lim - - 2x *→(π/2)- (2-) tan r Show all…

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Q: Determine whether f(x) approaches or as x approaches 6 from the left and from the right. f(x) = sec…

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Q: 16. Use properties of logarithms to expand log (²₁¹). t14

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Q: Suppose that a particle moves along a straight line with velocity v(t) = 7 - 3t, where 0 ≤ t ≤ 0.5…

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Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: 9. (a) Express 2 x4 – x² as partial fractions. (b) Hence, compute the exact value of the following…

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Q: Q4 (a) Calculate the surface integral: [] (² + (y² + 2yz) dS where o is the first octant of the…

A: To evaluate the surface integral Given plane 2x+y+2z=6

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Q: A spring is stretched 6 in by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism…

A: Given :The spring is stretched 6 in by a mass that weighs 8 lband damping constant…

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Q: The radius of a spherical tumor is growing by. centimeter per week. Find how rapidly the volume is…

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Q: Let f g and h be the functions defined below i. 11. f(x) = 5¹ = 10x₁ (²² = 4) g(x) = log5 h(x) = 6 x…

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Q: Let f(x) be defined by Find f'(1). f(x) = (2x - 1).

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Q: Let a-2-3j.kb-41-) and c-1-31-2k. If d is such that da-9. db-7 and dc-6, then d is equal to 01-31-2…

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Q: ขน lim (x,y) → (0,0) x² +10y²

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Q: the Factor Theorem to determine whether x+2 is a factor of P(x) = 2x² + 3x² +4. cifically, evaluate…

A: Here given that x+2 is factor of p(x)  so according to factor theorem x+2 is the factor of p(x) then…