Calculate the derivative d dx dx e5x In (t)dt using Part 2 of the Fundamental Theorem of Calculus. e5x fr8 In (t)dt = 18 Enclose arguments of functions in parentheses. For example, sin (2x).

Q: The following expression can be simplified to -1. 5x-3 3-5x 3 , where x + ³. O True о False

A: If the numerator and the denominator is same, it can be cancelled.

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A: Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population…

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Q: Calculate the derivative using Part 2 of the Fundamental Theorem of Calculus. X 21 d 1/² (316-1) ²¹…

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Q: Evaluate ¹₁7x8 - 2x³ + 3x² dr. Round your answer to two decimal places. ¹₁7x82x³ + 3x² dx = [Number…

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Q: Find f(x) if f'(x) = 5/1-x² and f ¹ f(²)=7 7. f(x) =

A: Given f'( x ) = 51 - x2f( 12 ) = 7

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Q: (2) Graph the polynomial P(x) = x³ + x² − 5x+3 using calculus by showing the given steps: (a) Find…

A: We need to solve function and draw graph.

Q: A restaurant purchased kitchen equipment on January 1, 2017. On January 1, 2019, the value of the…

A: A restaurant purchased kitchen equipment on January 1, 2017. On January 1, 2019, the…

Q: Multiply ◄ O x-2 x+4 x²-5x+6 x²+3x-4 O 1x-3 (x-2)(x+2) O (x-3) ² O 1 (x-3)(x-1) (x-3)2

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Q: Evaluate the indefinite integral. [x√3-x² dx

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Q: 3. If lim f(x) = 2, what is the value of lim x-1 a) 0 4. Evaluate lim 5. X-4 a) 5 b) 1 b) 4…

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Q: In Problems 1-10, solve the given differential equation by using an appropriate substitution. 8. dy…

A: To solve the following differential equation by using an appropriate substitution. dydx=x+3y3x+y…

Q: f(x, y) = ln(-6x – 4y), (5,6), A=6i + 8j 14 17 A) 135 135 B) C)/17 D) 11 135

A: Duf=∇f·uu

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A: Given that, a trapezoidal plate with height = h, Bases = a, 2a, and the weight density constant = δ.…

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A: We need to convert these rectangular to cylindrical coordinates

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A: As per company guidelines only one question is allowed to answer for multiple question posted.…

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Q: Use the Leading Coefficient test to determine the right and left end behavior of the following…

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Q: 5. Suppose the series anx" has radius of convergence 2 and the series bx" has radius of convergence…

A: The series ∑anxn has a radius of convergence 2 and the series ∑bnxn has a radius of convergence 3.…

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

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Q: m #10: Consider the following function. g(x, y) = e5x² + 8y² + 10√√6 x (a) Find the critical point…

A: We have to find the critical points  of the  given function.

Q: Find dx dy dx 11 d²y dx² x = t² + 3, y = t² + 9t = and d²y dx² For which values of t is the curve…

A: x=t2+3 , y=t2+9t

Q: 3. a. What is the domain of the function g(x)? Write the answer in interval notation. g(x) = log₂…

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Q: The populations P (in thousands) of a certain town in North Carolina, from 2006 through 2012 can be…

A: The population of a certain town in North carolina from 2006 to 2012 is given by:P(t)=4.2ektwhere…

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Q: Evaluate the definite integral ²₁ (2²-52) dz using the Fundamental Theorem of Calculus, Part 2.

A: Given integral ∫-12( x2 - 5x )dx = ?As we know that ∫xndx = xn+1n+1

Q: ENTERING INTERVAL ANSWERS For intervals of values, enter your answer using interval notation. Here…

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Q: Estimate the slope of the tangent line at the point x = 8, for f(x) = ln(x). (Use decimal notation.…

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Q: Find f(x) by solving the initial-value problem. f'(x) = 2e - 8x; f(0) = 5 f(x) =

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Q: 8) f(x, y) = 7xy² + 5xy-2y

A: We need to find the mentioned derivatives for the given function:

Q: Find the nth Maclaurin polynomial for the function. f(x): = 1 1- x n = 6

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Q: Find the general antiderivative. Use C for the constant of integration. g(0) = sec(40)tan(40). G(0)…

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Q: Use the Leading Coefficient test to determine the right and left end behavior of the following…

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Q: -10 foci Find the foci and asymptotes, asymptotes Find an equation for the hyperbola. -5 (x, y) =…

A: Now the equation of hyperbola is of the form:y2a2-x2b2=1Here a=6Therefore:y236-x2b2=1

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Q: Consider the following. f(x, y) = 4 YA 0 r = 1 + cos 0 D (a) Set up an iterated integral in polar…

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A: Accelaration at=8t-5

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Q: Find the limit. Use l'Hospital's rule where appropriate. If there is a more elementary method,…

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Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = ln(x2 + 7) Find the…

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Q: Determine whether the statement is true or false. 3 64 True False [/=.

A: Usinng integeral formula

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A: Given data Total length of fencing material is 240 feet.