Determine all values z ∈ C satisfying  e^z = −2i.

Q: Separate tanh-1(x+ iy) into real and imaginary parts.

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Q: Find the exact value. In 3 0 ³ sech 4 x tanh x dx

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Q: Find the linearization of ƒ(x) = √(x + 1) + sin x at x = 0. How is it related to the individual…

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Q: Use a linear approximation (or differentials) to estimate the given number.   sqrt(100.8)

A: Given that

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: 70ot(*) e*dx e2x +1

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Q: Define the term“constant integration”?

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Q: Use integration by parts to verify the reduction formula.

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Q: compute the derivative.

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Q: Verify the integration formulas ∫sech x dx = sin-1 (tanh x) + C

A: To verify: The integration formula, Formula used:

Q: - $x² cos(x³) dx

A:

Q: Find the theoretical error bound in approximating SN" sin(x?) dx using Boole's Rule.

A: The theoretical error bound in approximating the integral∫0πsinx2dx using Boole's rule is shown…

Q: b) write an expression for the position in terms of time t, use c (lower case) to denote constant of…

A: a =dv/dt where a is acceleration

Q: Verify the integration formulas ∫sech x dx = tan-1 (sinh x) + C

A: To evaluate ∫sech x dx

Q: Verify Eq. (2): cosh 2 x - sinh2 x = l.

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Q: Evaluate the indefinite integral. sec* (x)dx

A: We have to find the integral of sec^4(x)  Please see the explanation below

Q: sin 0 r (0) = log„(ršin ® – sin" 0)

A: We know that, from the derivative formulas ddxax=axloga       ⋯⋯1ddxlogx=1x…

Q: find integral sec 3 x dx

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Q: (log a) dx 1+x²

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Q: rIn 2 cosh x dx. Vsinh a x + 4 sinh x +2

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Q: find fsubxz if (x, y, z) = ye^x + x ln z

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Q: 3 sinº x dx 4 Show that

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Q: Find the interval in which function f(x)=sin (log,x)+cos(log,x) is decreasing

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Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

Q: What is the value of the function xcosnxdx if we integrate it using Kronecker' smethod?

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Q: Use an appropriate substitution to integrate 12 x*(x++ 1)°dx

A: The given integral is 12x3(x4+1)9.

Q: sin“ (x)dx 4

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Q: Find y" by implicit differentiation. 4x3 + 3y3 = 4 %3D

A: Given: 4x3+3y3 = 4 To find: The value of y'' by Implicit differentiation.

Q: Explain graphically why there is no solution to cosh x = sinh x

A: cosh x = sinh x. We need to explain graphically why there is no solution to the given equation.

Q: The integration of cosx is

A: Recall: Definition of Integration:      In mathematics , Integration is a technique to finding a…

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

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Q: Find the indefinite integral. ∫sec x/2 dx

A: Given ∫sec x/2 dx. We need to evaluate the above integral.

Q: Solve the nonhomogeneous ODE by variation of parameters. ODE: y" + 4y = cosh 2x

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Q: If f(x)-logCos4x + sinx.Then find 9 (x) JP at x= sec 2c dx 6.

A: Given function is: f(x)=logsec2x|cos4x|+|sinx| To find the value of 9df(x)dx at x=-π6

Q: Evaluate integral x^2e^-x^3 dx

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Q: Hw) Prove That:- 0 sinhz = log (z+lz*+) e coshz= Loy (2/23) ® Tanh'z = +2 1-2 Examml

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: 1 point) Calculate the integral: 1 dx = (x + 8)(x + 4)

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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: calculate the integral.

A: Given integral is We will use the following substitution to evaluate the integral

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

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Q: Find all extreme values for y=x+sinx^2 over [0,π]

A: Given,  y = x + sin2x  We have to find the extreme value in the interval 0, π

Q: tanh 2x In (cosh 2x)dx

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Q: if X #0 メ=ロ Frnd continuous

A: given the function fx=xx if x≠00   if x=0 we know that x=x if x>0x=-x if x<0 therefore,…

Q: for dx

A: Given integration is : ∫exdx To find the value given integration by parts.

Q: Solue this Logistic stochostic differentialegh where ajb,c constant wit) ;win er Process by using…

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Q: 19. Determine the derivative of f(x) = e* coshx. O a. e2x O b. ex O c. e4x O d. e5x

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Q: if 2 tanh x.In x = sinh' (sin x)+logcos dx dy Q5/ Find

A: To differentiate the given function.

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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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: