[Select] the derivative of y? y = x⁹e²x+1 18. Which rule is applicable when solving for A. Differentiation rules for natural exponential functions B. Differentiation rules for general exponential functions C. Differentiation rules for general logarithmic functions D. Differentiation rules for natural logarithmic functions [Select] A. y' = (e²+¹) (2x³ + 9x³) B. y = (2+1) (9x³) C. y = (2x³e²+¹) D.y = (e²+1 +928) 19. Which equation is the derivative of y?

Q: Evaluate the following integrals / limit/s: 1. S√16-x²dx dz S. 2. √x²+2x

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Q: R is the region bounded by the functions f(x) = 3x² + 27x + 54 and g(x) = -3²-22-27. Find the area A…

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Q: dy = 26² Q2/B) Solve the following differential equation by using homogenous D.E method dx

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Q: 20. S dr √3-4r-r²

A: On solving this we will get

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Q: Consider the curve, x² - y² + sin (TX) In(x) + x = 0. =

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Q: The derivative of f(x) with respect to x is the function f'(x) and is defined as f'(x) = lim 0…

A: To find f(x+h) replace x by x+h in f(x).

Q: which is TR

A: We have to choose the correct option from the given options according to the given information

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Q: QUESTION 13 Is this statement true or false? An infinite sequence (a) is convergent only if lim a, =…

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Q: 4. Express the following in cartesian form. 2 2 cos 03 sin

A: Given r=22cosθ-3sinθTo express in cartesian form:

Q: Lemma*: If z(x, y) = W+H, then xZx + y2y = (xWx+yWy) + (xHx + yHy).

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Q: 2xy π Find the equation of the tangent line of the function tan (xy²) = " at x = π

A: This question is based on finding tangent equation while calculating slope.

Q: X 17. 7. So (x²+ + 2)² dx

A: Topic = Integration

Q: fax² ax² + bx dx is equal to O ax³ bx² ㅇㅇ + C 3 2 ax³ bx² 3 2 a²x³ 6²x² 3 2 a²x² 6²² 3 2 O + + + +…

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Q: 5. In another state, license plates are formed using 6 symbols, any of which can be a number of a…

A: We know, There are 26 letters A, B, C, . . . , Z and 10 numbers 0, 1 , 2 , . . ., 9.Therefore we…

Q: If f'(x) > 0 at x = c, f(x) at x = c is

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Q: 2x²+x+1 S (x− 1)(x + 1)(x − 2) dx = ₁ 11 (A) 3 (B) None 11 C 3 (D) -SA+ 1 3 E -2 B + x+1 x-2 Q dx,…

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Q: Which of the following is or is not an improper integral? Clearly explain your choice. A. ₂ dx B.…

A: improper integral means whose limit at any point goes to infinite  here check for it. ∫1dx/(x-2) =…

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A: We need to find area.

Q: DETAILS LARPCALCLIM4HS 5.3.063. Solve the equation. (Enter your answers as a comma-separated list.…

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A: I am attaching image so that you understand each and every step.

Q: Which statement is TRUE about trigonometric functions? O a. The derivative of sin x, cos x and tan x…

A: The answer with explanation is given below:

Q: f(x) = √√/5x+8 What is the derivative of f(x)?

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Q: A radioactive substance decays exponentially. A scientist begins with 140 milligrams of a…

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Q: Using chain rule, what is the (2x-¹-3x)³ ? da O 24+108x²+54xª+81x6 x4 -24+36x²+54x4 -81x6 x4 O…

A: The objective of the question is find the derivative .

Q: 3. Test the following series for being convergent or divergent: (2) Σ < (3n)! n!(+1)!(+2)! (c) Σ…

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Q: 1. Find the inverse of 3x + 1 = 4. x-1 (1) y = x (2) x = y-1 10 (3) x = 3y + 1 (4) y = x+1

A: Given :3x+1=ythenf(x)=y=3x+1

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Q: For the function z = x² +2y²-4x+4y, which of the following statements is true? O a. The function z…

A: Given,  z=x2+2y2-4x+4y

Q: e Sc (4x + 3√y) c Evaluate figure. ds where C is given in the accompanying CH 1- (0,0) y=x O (1,1) X…

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Q: Find the derivative of the following functions by using the limit definition of the derivative.…

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Q: f(x)=√√3x² +6x+2

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Q: Suppose the functions heas and reas are defined follows beas = 5x=2x² rexlx23x4 X+2 -2 Write down Oh…

A: We have to solve the given inequalities.

Q: figure out absolute min & max values: g(x)=cos^2(x)-3sin(x) Interval:0<=x<=pi

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Q: 3 | co - 4. Find the length of the curve y = 7(6+ x)2 from x = 189 to x = 875.

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Q: Calculate the centroid coordinates of quarter circle (x² + y² = a*) in the quadrant, use Cartesian…

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Q: If an investment grew to $13,500 in 3 years and the interest amount earned was $1,531.34, calculate…

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Q: ffff dydadz, where A is the region of hemisphere A ² + y² +2²=a²is the same as tripple integral by…

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Q: 16. dx x√√16+x²

A: To find out the integration.

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Q: Evaluate and Solve the function using the product rule or quotient rule. Show your complete…

A: Our Aim is to evaluate and solve the function given below using quotient rule.y=2x3-35x+2 -(i)

Q: If 10 fro A True B) False f(x) dx = 17 and 8 Lof(x) d f(x) dx = 12, then 10 ["fo f(x) dx=5

A: ∫010 f(x)dx = 17 ∫08 f(x)dx = 12 ∫810 f(x)dx = 5

Q: (x - 8)dx x (x + 5)² X

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Q: Let f(x) = 3 cos 2x + sin² x. a) Show that f'(x) = -5 sin 2x. 3π b) In the interval 프 <x< 4 one…

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Q: The plane (x, y, z) = (4, 2, 1) + s(1, 1, -2) + t(2, -1, 3), converted into scalar form, has the…

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Q: S (x - 8)dx x (x + 5)²

A: see below the answer and calculation

Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C