What is f'(0)? f(x) = (7x4) (3x+8)4

Q: 1. Explain two different ways to solve for the derivative of s(0) = 200sin cos

A: Topic = Derivative

Q: 40 For problems 21 function to find t C 123, use the following. following rut o

A: We will find the required.

Q: : x-2y+3z-1 = 0 and the line 1 : x = Consider the plane 1. Find the point of intersection of and 1.…

A: Given: x-2y+3z-1=0x=1-y2=z+1

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 300…

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Q: Consider the parabola f(x) = -x² - 4x-7 i) Write the equation in vertex form. ii) Find the vertex…

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Q: Consider the smooth parametric curve 6 defined by the equations t (t²-3) { 3 (t²- 3)' = = where t€…

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Q: 5) Integrate 2x cos (x²-5) with respect to x.

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Q: 1. Consider the region R bounded by the functions f(x)=3x and g(x)=x²+2. The centroid of R is: a.…

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Q: Use the limit definition to find the instantaneous rate of change of f(x) = 3x^3 - 4x at x= -3

A: Question is solved.

Q: A formula for the relationship between weight and blood pressure in children is given by the formula…

A: Let's find rate of change of blood pressure.

Q: What is 30,264,836 times 97,125,356 ?

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Q: S √x²-a² X dx

A: To solve the given integral.

Q: A D 1. Determine an expression for the area of a rectangle inscribed in a circle of radius 1 cm, in…

A: Explained below

Q: 2 x²√x²+9 dx

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Q: Determine for the following function: dy dx y = log3 (x² + 1) ○ (z²+1) In 3 2x O (1²+1) 2x O 2x…

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Q: [xt xtan xdx

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Q: ● ftan(x) sec(x) dx

A: We will use substitute method to solve the integration

Q: Find the area of the region enclosed by y = 6x² and y = x² + 1. Round your answer to three decima…

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Q: 10. Find function that satisfies the given conditions: f"(x)=6x³-3x+4, f'(1)=-3, f(1) = -6

A: The function satisfies the condition f''x=6x3-3x+4, f'(1)=-3, f(1)=-6 use the integration formulas,…

Q: why is V e3x3? and pls write the solution in a paper instead of typing digitally to understand the…

A: Let's solve integration.

Q: 2. Use the process of implicit differentiation to find given that: 52³² + 3 = 5xy. Apply implicit…

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Q: s) Given the piecewise function below, find h(-5) and h(-4). if x < -4 h(x) = { 6x - 7 √x+8 ifx ≥-4…

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Q: Jacob's father is planning to open a savings account to pay for Jacob's college education. He has…

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Q: Find the partial derivatives (f, and fy) of the below function and simplify your answe f(ru) = (ru)2…

A: Topic:- application of derivatives

Q: -5 2 y=f" (x) A description of the graph of f(x) would be: a 4th degree polynomial a downward…

A: There is a given linear graph representation of second derivative f''(x) of a function as f(x). We…

Q: A tank contains 70 kg of salt and 2000 L of water. A solution of a concentration 0.0175 kg of salt…

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Q: 76 6 27 6 Σ [5 (2 + (i - 1) =) * - 7 (2 + (x − 1))"] n n as a definite integral, that is provide a,…

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Q: 3 ¹₁ (4x² + 7x²) dz 1 Find

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Q: 5. Using f(x)=xln√x + 2x; Do each of the following: Find f(x) and f(x) a. b. Find critical values…

A: The given function is fx=x lnx+2x we have to find f'x and f''x use the derivative formulas,…

Q: Praw the curve r= 4 + 8 case and find the area outside the inner loop of the curve

A: Given: r=4+8cosθ

Q: for problems 16 and 17, use the following. the following rule of func f(x)= x² + 4x² +2 to find 75…

A: Given: f(x)=x3+4x2+2

Q: Find f'(x) and find the equation of the line tangent to the graph of f at the indicated value of x.…

A: Here is the solution:

Q: (i) Consider the function f: R\{-2,3} → R defined by 2x³4x²5x - 3 x²-x-6 f(x)= - (a) Prove, using…

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Q: -5 0x2 0<x<2 2 Over what interval is f(x) concave down? Ox<0 y=f" (x) 5

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Q: . Let f be a function of two variables such that and f(2, 1) = 4. af Ət If, in addition, x = r cost…

A: The given gradient of the scalar function fx,y is ∇→fx, y=3x2-3y, -3x+3y2. Also, we have f2,1=4.…

Q: dr 4+x² S Choices: tan ¹(x + 2) + C 1 In x² + 4 +C In x + 2+ C 1 tan 2 1 ¹ 1/2 + +C

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Q: Find the value of the given limit. lim I 0 tan(4x) I

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Q: Obtain the family solutions. (5v-u) du + (3v-7u) dv = 0

A: We asked to find the family of the curves

Q: tiderivative. Indicate which formula from the that you may have to do a substitution, or a tables!…

A: Ass per the guideline I am answering only one question at a time. ∫tan3x2dx

Q: Which statement would be represented by an inequality? To ride the roller coaster you must be at…

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Q: Find the exact average value fave of f(x) [0,5] where f(c) = fave. fave = C= Submit Question = 25-2…

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Q: The area of the surface formed by revolving the curve x = 2√1-y in the interval 0 ≤ y ≤ 1 about the…

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Q: By an appropriate trigonometric substitution, Choices: √ √10 sin sin 0 cos de cos √10 sin 0 1 /10…

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Q: Q/ Evaluate the following integrals. S f sec40 tan²0 de

A: W have to find the integral.

Q: S 1 (x²+6x+5)3/2 dx

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Q: A company manufactures mountain bikes. The research department produced the marginal cost function…

A: Here is the solution:

Q: Q2:A: Find the surface area of the cone y = h -√x² + z² where h is the height of the cone and a is…

A: Concept: The surface area of the cone: The total area that a cone's two surfaces, its circular base…

Q: The decay rate for a radioactive isotope is 1.6% per year. Find the half-life

A: Given that the decay rate for a radioactive isotope is 1.6% per year.Our Aim is to find the…

Q: Find and sketch the domain of f(x,y)=√1-(x + 1)² - y² + 2ln(x -y + 1)

A: Let's find domain of given function.

Q: Find the area of the surface given by z = f(x, y) that lies above the region R. 3 + 6x3/2 f(x, y) R:…

A: In this question, we need to find the area of the surface.