The slope of the line normal to the curve ex- x³ + y2 =10 at the point (0, 3) is: A. -1/6 B. 1/6 C. 6 D. -6 E. Undefined

Q: Find the directional derivative of the function at the point P in the direction of the point Q. f(x,…

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Q: Find Vf at the given point. f(x,y,z)=x² + y² - 3z²+z Inx. (1,4,3) Vf|(1,4,3)+(+(k (Simplify your…

A: Given:We are required to find:

Q: Consider the curve y = x² + 3x + 5. Find the slope of the secant line at the point where x = 9. Oh…

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Q: Given f(x) = 2x² + 1 and g(x) = 4x - = 4x - 6, find the following. (a) f(g(2)) (b) f(g(x)) (c)…

A: Given functions are,Under guidelines we are suppose to answer only 1 or 3 sub parts.

Q: Find the Volume V(S) of the solid S generated by given R: R is the region bounded by y=6-x² and…

A: To find the volume  of the solid S generated by given R: R is the region bounded by  and  and it is…

Q: 7. Given f(x) = ax² + bx + c, determine the values of a, b, and c if: f'(x) = 6x + 3 and ƒ(2) = −1.

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Q: = Find the maximum and minimum values of the function f(x, y) = x² + y² ≤ 225. The maximum value of…

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Q: the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the points…

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Q: Questions #8 to #12 pertain to the accompanying Venn diagram. 8. If n(AUB) = 40, what is the value…

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Q: The plane x + y + 2z = 10 intersects the paraboloid z = x² + y² in an ellipse. Find the points on…

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Q: Given f(x, y): fz(2, 3) - fy(2, 3) = -4x¹ +5xy² + 2y³, find the following numerical values:

A: The given function is; f(x,y)=-4x4+5xy2+2y3Find fx(2,3) and fy(2,3).

Q: Salue the trig equations on 040127 1+COSA = =

A: 1+cos(theta)=1/2, 0<=theta=<2piFind the value of theta lies in the given interval.

Q: Suppose that h(x) is an unknown function with the following properties: ex x² ● h'(x) - h(1) = 3 Use…

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Q: If ƒ(4) = 3 and fƒ'(4) = −5, find g'(4) where g(x) = √xƒ(x).

A: To find g'(4) where g(x) = sqrt(x).f(x)  also given f(4)=3 and f'(4)=-5Derivative using product rule…

Q: Using the change of base formula, log, 10=7 log log(10) O In(20) O A h (10) O bg (10) log

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Q: Find the indefinite integral. 9x8 +9 [... (x⁹ + 9x)² dx

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Q: Find an equation for the line tangent to the curve y = (√x - 9)(x³. 6) at x = 1.

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Q: The demand functions for two products are given below. P1, P2, 91, and q2 are the prices (in…

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Q: For the following system to be consistent, 3x-6y + 7z + kz - 3z 13x- Oy -2x-9y we must have, k ‡ = -…

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Q: Compute the derivative of f(x) = e^x/ x^n for constant n using the specified methods: (a) The…

A: Use the product rules of the derivative is d/dx(uv)=u*(dv/dx)+v(du/dx) And quotient rulesd/dx…

Q: 2. Which polar coordinate pairs label the same point? a. (-2, π/3) b. (2,-π/3) c. (r, 0) d. (r, 0 +…

A: We have to find the pair that labels the same point in polar coordinates.According to our guidelines…

Q: Simplify the following expressions. sin x sec x sec² x-tan²x+cot² x sin² x cos 2x-cosx sin 2x+sin x

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Q: if both f (x) and g (x) are differentiable, then d d [ƒ(x). 9(x)] = f'(x). g' (x). O True O False

A: given both f(x) and g(x) are differentiable.

Q: For what values of x does ƒ(x) = x - sinä have a slope of 1 on the interval [0, π] ? O O K|+ T 4 π…

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Q: Find the first partial derivatives of the following function. 8u 5v + 7w F(u,v,w)= F₁ = Fu

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Q: 15 years ago, a company started depositing money into an investment account earning interest at an…

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Q: The number of children in a church is increasing at a rate that is proportional to the number of…

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Q: At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of…

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Q: 1. Solve for x. 5 4 2x + ²/2 = 7 - x. 9 3

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Q: Suppose 3x² + 4x + xy = 3 and y(3) = = y'(3) = -12. Find:

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Q: The Cobb-Douglas Production function for a certain company is given by P(L,K)= 1400L ^0.7 K^0.3…

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Q: e) g(x) = (4x²+8)(3x4 - 11x² + 5)

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Q: Many populations are facing negative growth rates. If the population of the Ukraine was 60 million…

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Q: । -2 3 -3 2 4 6 j (.) 8 10 I

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Q: 25. Determine the value of k so that f(x) is continuous. Show work. x² - k 2x² + 7x-22 x≤2 x>2 x-2…

A: A function f(x) is said to be continuous at a point a, if Left hand limit and right hand limit and…

Q: We have determined that A = 36 and B = -6. Therefore, we have the following. A 6x + 1 30 (6x + 1)(x…

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Q: :. Calculate the total amount of interest earned from this investment during the 4-year period.

A: The amount invested, P=$13000Interest rate, i=5%Compounded frequency, m=2 (semi-annually)

Q: It is determinate because there is only one known force. It is determinate because there are no…

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Q: At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of…

A: Note:- As per our guidelines, we are supposed to answer only one question with a maximum of three…

Q: The graph of y = f(x) is graphed below. What is the end behavior of f(x)? 6.4 5.6 4.8 4 3.2 2.4 1.6…

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Q: Suppose xe¹ - 4y = 3x + 1 + le¯¹ and y(1) = -1. Find: y (1) =

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Q: How is the product of a complex number and a real number represented on the coordinate plane? When 6…

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Q: Given the initial condition y(0) = 2, find the particular solution of the equation e'y' - 2x = 0

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Q: Which equation is the polar equivalent to the equation y = -√√3x? 0 = O 0 = Col 0 0 = 25 0 0 = 5T

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Q: Given the Pythagorean theorem a² + b² = c² where a and b are the lengths of the perpendicular sides…

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Q: Suppose lim f(x) = = x→2 1/2 4 -5, find lim x→2 x²| ƒ(x) + 6 x - 1

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Q: Instruction: MAT 143: Algebra and Trigonometry ✓Answer Must be Handwritten ✓ Question No: 2 question…

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Q: se a software program or a graphing utility and Cramer's Rule to solve (if possible) the system of…

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Q: Find the Volume V(S) of the solid S generated by given R: R is the region bounded by x²+y-4=0 and…

A: To find the volume of the solid S generated by revolving the region R about the line x=-2, we can…

Q: you know that a sphere has the equation of  x^2 + y^2 +z^2 -6x +4z =3 are the following points…

A: The equation of sphere is:-Now add 9 and 4 both side:-