Find the derivative of: -5e-3 cos(5x). [Hint: use product rule and chain rule!] Use e^x for e. 4 Now, find the equation of the tangent line to the curve at = 0. Write your answer in mx + b format. y =

Q: IF y = u+ + 3u2 & u = 3x Find dy dX

A: If y=f(u) and u=g(x),thendydx=dydu.dudx dundu=n.un-1

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: Given:-f(x)=3+3x-3x2 ; 0, 3f'(x)=3-6xfor critical pointsf'(x)=03-6x=06x=3x=36=12second derivative…

Q: For the function, find the points on the graph at which the tangent line is horizontal. If none…

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Q: b) lim x²-25 X-4 X+5

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Q: 7* +(7)*. 2 7. If А. 2 О А О в О с O D = 1 then x= В. 4 С. -1 D. 0

A: We will find the value of x in the following step.

Q: Draw a graph to match the description given. G(x) is decreasing over (-∞0,0) and (8,00) and…

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Q: B. Find the general solution of the following differential equation xyy' = ¹+y² 2 1 100

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Q: Ax 10.5 7.1 × де 400 = x + What is the value А ? д - 10.5 3.1 - 7.1А -

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Q: Use the properties of logarithms to expand the logarithm as much as possible. Rewrite the expression…

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Q: Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of…

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Q: Find the area under the given curve over the indicated interval. y=x²; [0,5] The area under the…

A: Given: Now, we need to find the area under the given curve.          Area = ∫05x2dx          =x3305…

Q: Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate…

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Q: Q3 Answer these questions and choose the correct answer ALIM 0 1 2 is a matrix then find the M¹ 1 2…

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Q: x + y + z = 1 2 + 2 + 2 = 2 3 + 13 + 23 = 3 = 7 5 + + 5 + 2 9 = ? =

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Q: C. Find y for the following: 1) y = x¹e³x tanx e4x 2) y = x³ cos2x 3) y = xx.sinx

A: Given: (1)  y = x4e3xtanx (2)  y = e4xx3cos2x (3)   y = xx· sinx

Q: -28 5. How is can be express as rational number with numerated the number 47 84 O 4/7 O-4/12 - 4/7…

A: Given query is to re write the expression as numerator with 4.

Q: ator of a sphere, parameterized by spherical coordinates 0, and p. Let "north" point to the top

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Q: For what values of x does the series below converge? What is its sum? What series do you get if you…

A: We have to find the sum and derivative of the series.

Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: ) Write a MATLAB code for solving the following equation : N Y = [i+x i=1

A: MATLAB code

Q: Q3/ Evaluate four of the following integrals. a. S sinx cosx 1+cos2x dx_b. f*¹ dx c x²

A: INTEGRATION

Q: LO 5 100 160 500 √√25 O +1 O -1 O +1,-1 None of them

A: We can find the solution as below.

Q: Differentiate the function. y = (2x-5)³ (5-x4) 4 dy dx

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Q: Evaluate 3 (9x² - (0x+6) dx 2

A: Given query is to find the value of the integral.

Q: 5- A virus is spreading according to the function p(t) = 125(2)¹/4, where p(t) is the number of…

A: This question is related to Functions and rate of change, we will solve it using given information.

Q: A linear function is given. g(x) = -9x + 5 (a) Find the average rate of change of the function…

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Q: Find the maximum and minimum limits of the function f(x) = - X-2 (x+2)²

A: Given ,f(x)=x-2(x+2)2We know that ,Suppose that x=c is a critical point of fx then, If f 'x<0 to…

Q: Consider the differential equation 2xy" - 3y + 3y +³/4 = 0 (1) It turns out that y₁ = r is a…

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Q: 6- For the function y=lnx a- Describe what type of function it is. b- How is the function related to…

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Q: Draw a graph to match the description given. f(x) has a negative derivative over (-∞,5) and (5,9), a…

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Q: 5. -9.763332111 is a Whole number. True false 6. (0.01) 365 > (1.00) 365 True false 7. (2²²)⁰+ (2⁰…

A: 5. Given , -9.76332111 we need to say wether given number is a whole number or not definition of…

Q: 1. The value of (1.000) 27 is O 327 O 0.327 O 1.000 O Non of them

A: Any finite power of 1 gives you 1.

Q: Compute the total area A of the (infinitely many) triangles in the figure, if the height h of each…

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Q: 3. Sketch the graph of one function f(x) that has all of the following properties: a.) The domain of…

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Q: (c) Runge-Kutta method Compare the %error of the estimate values of (d). Show complete solutio

A: answer is in next step

Q: If f f(x) dx = 2, and f f(x) dx = -5, then, So f(x) dx =

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Q: In 2012, 34.1% of all glass containers were recycled. A beverage company used 350,000 lb of glass…

A: We need to fill in correct answer.

Q: O O ΑΠΦ=Φ. True false

A: Let A be any set. We know that,  For any set A, the null set is a union of A. For any set A, the…

Q: If f is differentiable and f'(x)=x³-2x²-x+2, then fis increasing or

A: Given, x³−2x²−x+2=f' We equate the given function to zero for critical points. x³−2x²−x+2=0   Step…

Q: what is the basic concept of a derivative? How is this derivative calculated? What techniques/rules…

A: Use the definition of derivative

Q: 16. In circle Z, if VZ = ZW, SV = 21, and mUT = 112°, find each measure. a) UT = x d) mXT W b) WT =…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: f(x) = 9x²

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Q: IF y = u+ + 3u2 & u = 2x Find dx

A: Chain Rule of differentiation : If y=f(u) and u= g(x) , then         dydx =dydu.dudx

Q: dw H.W: Use the chain rule to find the derivative dt with x = cos x = cos² t, y = sin² == and…

A: Given :w=xz+yzx=cos2t    and y=sin2t   z=1t

Q: 1. The value of (1.000) 27 is O 327 0.327 O 1.000 O Non of them (242²-121²) 242*121 O 1 O 2/3 O 11/3…

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Q: Directions: Give the answer completely. Show the graph and the plane region in the Cartesian plane.…

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Q: Find the area bounded by the parabolas y2 = 4x and x2 = 4y

A: Given curve: y2 = 4x and x2 = 4y To find the area between y2 = 4x and x2 = 4y First find the…

Q: Suppose that F(x) is a function such that F"(x) = f(x). Which of the following statements is true? […

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Q: T/F: The function y(t) = Pert-rt is a soln to s differential equation dy/dt = ry where P and r are…

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Q: Solve y'= 3y.x² 3 x³ + 2y4

A: This question can be solved using the concept of linear differential equation.