Find the first six terms of the expansion of the function e^x log(1+ y)

Q: > Evaluate the Antegral dx ax45x +2

A: Rewrite the given integrand as follows. 32x2+5x+2=32x+1x+2=22x+1-1x+2

Q: What happens in Newton’s Method if your initial guess happens to be a local min or max of f ?

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Q: If the population of penguins on the island in year 0 was 10,000, what is the population of penguins…

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Q: Evaluate cosh #j in 3 decimal places.

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Q: ln(x) is just defined for x greater than 1. Select one: True False

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Q: Verify the power rule for integration n+1

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Q: Use differentials to estimate (2.03)4

A: Given: To find differentials to estimate (2.03)4

Q: Determine the positive real root of ln(x^2)=0.7 using three iterations of bisection and…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: where did 0.025 come from? please explain the steps to get critical value

A: The level of significance is 0.05.

Q: Select a suitable technique for each indefinite integral. (Justify) Solve for each integral.

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Q: Tomorrow a sum of PhPI0,000 will be invested at rate R. Tomorrow's rate is unknown at the moment, so…

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Q: ou have an opportunity to buy a business that will earn $10,000 per year continuously over the next…

A: To find: The present value of the business. Given information: A business that will earn $10,000 per…

Q: The integ ral csc(0.5) dx is equal to

A: Follow the procedure given below.

Q: Differentiate  f(x)  = log 10  ( 2+ sinx )

A: Rewrite the given function as shown below: fx=log102+sinxfx=ln2+sinxln10        since logab=lnblna

Q: Find the indefinite integral and check the result by differentiation. dt F--3-3)- 8. 12

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Q: dr 3. Verify that = ln(2). x(x+1) 1

A: Given: ∫1∞dxxx+1=ln2

Q: Sitsux dx + sin

A: The given integral is: ∫(1+sin2x)dx=∫dx+∫sin2x…

Q: : Find value of x if :- 2 sinh (2x) - 4 cosh (2x) = - 4

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Q: tan x dx = In|sec x|+ C

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Q: Compute coshx and tanhx, assuming that sinhx = 0.8.

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Q: 3x ン

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Q: What is ln(-3)? Explain.

A: We  have given ln-3. We know that lnx is defined if x>0. Domain of lnx is (0,∞). Therefore, input…

Q: logtan nx(2+ 4 cos nx) 2

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Q: Verify the identity. sinh2 x = (−1 + cosh 2x) /2

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Q: Use the mean-value Theorem to prove 1 1 - < ln(x + 1) − ln x < - X x +1

A: Consider the function f(x)=ln(x) So, f(x) is continuous on 0,∞ and f(x) is differentiable on 0,∞.…

Q: find the fourier series for the half-Period sine of the function fx) = sinx inthe period 8. xx Then…

A: Given that, f(x)=sinx in the period 0&lt;x&lt;π. ∫n=1∞1(2n-1)2(2n-1)2. The objective is to evaluate…

Q: Find the indefinite integral.

A: Use the substitution method and consider x2 as u. Differentiate both sides of u=x2 and substitute x2…

Q: Find y' by ased proportici Ln Xャ3

A: Taking natural log both side

Q: Verify the identity by transforming the lefthand side into the right-hand side.

A: Consider the given equation. logtanθ=logsinθ-logcosθ Take all the value right side of the equation.…

Q: The graphs of y = 1/x and y = 1/ln(x) are shown at right. 2.0 15 a) Set up fully, but do not…

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Q: Use a linear approximation (or differentials) to estimate the given number. 99.8

A: To find √99.8

Q: | Suppose that the net earnings of a particular company at time t are being generated at the rate of…

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Q: Compute the fourth derivative of cos(x+1) - ln(x²+4) + x²²+1 with respect to x. Also, compute the…

A: Sol:- First part:- Fourth Derivative of given function:-…

Q: I Braluate th FOllowing integralis 3+cos (logqx) dx x sin (loga x )

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Q: 3:Use Gamma & Beta properties to evaluate : f (In x)³ dx

A: The gamma function is Γ(z)=∫0∞e-ttz-1dṭ The Gamma function is a non-integer generalization of the…

Q: Prove that the arc y = log secx from les (2+ 3

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Q: Use a linear approximation (or differentials) to estimate the given number. 99.6

A: Given query is to perform linear approximation on given redical.

Q: The first derivative of the power series 3x2 3x f(x) = 3 1! 3x3 3x4 325 %3D - 2! 3! 4! 5! • is

A: Formulae: 1. e-x = 1-x/1! +x2/2! - x3/3! +x4/4!- ....... 2. d/dx{ e-x} = - e-x   Answer: f'(x)= f(x)

Q: If x >0, Prove that X - ln (1+x ) > x^2/2+2x

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Q: * limt (x-sinx)\ x+1 10 log x^2+3 O 0.5

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Q: Evaluate ( Sech²(In x) dx

A: In this question we will use basic of calculus i.e concept of integration. First we will convert the…

Q: 3. Use Log Rule to integrate. J6x-5 dx a. 6х-5 b. S- 1 dx x Inx

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Q: Use a linear approximation (or differentials) to  estimate the given number.    cube root of 1001

A: Given: 10013 or 100113

Q: (1-x²)-1/2 Arcsin x

A: We will integrate the given function using simple Integration method.

Q: 1- Y= sin( coshx log2 2 ) 2-Y= sinx.coshx. log2 2 3 - y = In Vx. sin x

A: Apologize  that we are permit to do first question of the multiple questions but still I am doing it…

Q: Prove 42 tan xdx =1-log 2

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Q: 1 dx xln* (ex)

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Q: Find the indefinite integral ∫sec 4x dx

A: the given indefinite integral is: ∫sec4x dx we have to find the value of the given indefinite…

Q: To evaluate the integral cotx log(sinx) dx we use the substitution O a. sinx=t O b. logx=t O c.…

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