If f(x) = x(2^x), then f'(x) is equal to: %3D O 2^x (In 2+ 1) O 2^x (2 In 2 + x) 2^x (x In 2 + 1) O 2^x (2x In x+ 1)

Q: give 3 examples of the reciprocal rule of integration formula

A: The reciprocal rule for the integration is: ∫f'(x)f(x)dx=ln |f(x)|+C

Q: Find the derivative of Log(2z³). 2/z 2/2? 1/2? 3/z

A: Answer

Q: Show that √(10x + 1) and √(x + 1) grow at the same rate asx→ ∞ by showing that they both grow at the…

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Q: 3.

A: Indefinite Integration

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

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Q: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

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Q: tion, what is the longest time within whic at the predator will have to spend more t

A: It is found that the time (in minutes) required by predator to find a prey is a random variable that…

Q: A coat of paint of thickness 0.03 cm is to be applied uniformly to the faces of a cube of edge 29…

A: Let the side length of the cube be S = 29.Side increase on each side = 0.03 cm.Total increase in…

Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: x³tanh² (x*) sech²(x*) dx

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Q: 3. f Arccos 2xdx

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Q: One side of a right triangle is 150 m long and its adjacent angle is π/3 radians, with π/60 radians…

A: Possible error

Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: What are the formulas for differentiation and intergration? When to use them?

A: Query- What are the formulas for differentiation and intergration and describe When to use them?…

Q: Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

A: the fiven function is f(x)=ln(x)

Q: 4. Describes the various ways in which integration and differentiation may be viewed as inverse…

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Q: Find indefinite integral.

A: Let the given integral be y - y = ∫x12+3x-23 dx      Identity to be used - ∫xndx = xn+1n+1+C

Q: Use forward, backward and central difference to estimate the first derivative of f(x) = In(x) at x =…

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Q: What is the connection of the concept of limits to slope to derivatives (delta method to simple…

A: The limits of the function at a point are calculated using the formula . The limits are used to…

Q: Log Activity CALL l.y=log4 (3x2 -5x) In 9x4 2.y= 3.y= Inx3 X-5

A:

Q: What are the formulas for differentiation and integration? How are they applied?

A: To write: Formulas for differentiation and integration.

Q: dervivative of (ln(cosh(x)))3

A: Given data:     The given function is: y=(ln(cosh(x)))3. STEP-1 Assume u=coshx and differentiate it…

Q: 4. Find at the point (1,1,1) if ln(xyz) = 1 əx

A:

Q: The average annual increment in the horn length (in centimeters) of bighorn rams born in recent…

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

A:

Q: find integral sec 3 x dx

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Q: Compute Anti-Derivative (-1 --> 1)  (x^3 + x) / (cos(x) + pi) dx

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Q: Compute sin x dx er + 3e -x 8.

A: We have to compute the given expression ∫sinxex+3e-xdx from -∞ to ∞ Therefore, The  given expression…

Q: 8. The value of f sinh* x cosh³ x dx

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Q: 1. 8rd Derivative of fC x) = 4 x³ - 8x5 1

A: We will use just the basic knowledge of differential calculus to answer this question step-wise.

Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

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: What is the difference of antidifferentiation and anti-derivative?

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Q: Find:  ∫cosh^4 (x) sinh^5 (x) dx.

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Q: Compute the derivative. Use logarithmic differentiation where appropriate. 10 1+ dx 10 1+ dx 10 In…

A: Answer: ddx1+10xx = ln1+10x-10x+10 1+10xx

Q: A piece of wire, 370 cm long, is to be bent into an isosceles triangle. What should the exact…

A: given: A piece of wire, 370 cm long, is bent into an isosceles triangle. we have to determine what…

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

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Q: Use differentials to approximate the value of s2.1. O 100+6ln5 4 O 50+5ln5 2. O 100+5ln5 4. O…

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Q: water leaking onto a floor creates a circular pool with an area that increases at the rate of 3…

A: Let  A=π r2 differentiating A with respect to time tdAdt=2πr…

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

A:

Q: What is something interesting about integrationa and derivatives? Why is it interesting?

A: Given What is something interesting about integration and derivatives? Why is it interesting?

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: Find the indefinite integral ∫ x2 sech2 x3 dx

A: We have to find indefinite intrgral  ∫x2sech2x3dx We have ∫x2sech2x3dx  Take x3=t⇒3x2dx=dt⇒x2dx=13dt…

Q: ㅠ -π sec xdx. 3

A:

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

A: To differentiate the given function.

Q: What are the real-life applications of antidifferentiation or integrat

A: What are the real-life applications of anti-differentiation or integration?

Q: From a numerical perspective integration is better conditioned than differentiation.

A: As given, We have to state that whether the below statement is true or false. From a numerical…

Q: 3. SIX f- - dx x in x√√(inx)2-9

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Q: 8. Scoth 2x In (sinh 2x) dx

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Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

A: