Let f(x) = In(x) and g(x) = log2x. For all 0 g(x) O True O False

Q: What is the component form of the vector represented by 6a when a = (-2, 3)? 6a =

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Q: Find the derivative of y = -10x¹ sin (2x) + e cos 2x

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Q: Find the indefinite integral and check the result by differentiating. 5x (5)dx S₂5x (5)dx=

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Q: A cheesecake has equally sized slices. Each slice is a different flavor. The diameter of the…

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Q: 5C AND D

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Q: If you were given a conic section in general form, how would you determine what type of conic…

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Q: Find a closed-form expression for the nth derivative of the function h(x) = xeª. (Hint: Find the…

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Q: 6. f(x) = X a. lim f(x) x-0* b. lim f(x) X-0 c. lim f(x) X-0

A: f(x)=|x|/xFind the limit at 0.Find the right hand limit and left hand limit at 0.

Q: 4. x-6 3 a) Determine the point of intersection of the two lines. b) Determine the acute angle…

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Q: (e) Separating out the K and J terms, you now have a term of the form and bottom by a constant you…

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Q: Assume that F(x,y,z(x,y)) = 0 implicitly defines z as a differentiable function of x and y. The…

A: Assume that  implicitly define  as a differentiable function of  and .The partial derivatives of…

Q: Find f(a), f(a+h), and the difference quotient _f(a + h) − f(a), where h‡ 0. h f(x) = 9x² + 8 f(a)…

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Q: Prove the formula for d dx d [arccos x] in the same manner used for [arcsin x] in class. dx

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Q: The polar equation r = 6 sin (40) graphs as a rose What is the length of the petals of this rose?…

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Q: Express the function G in the form fo g. (There is more than one correct answer. The function is of…

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Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of…

A: As per the guidelines, I am providing the solution to the first question.

Q: ) An object is pulled with a 5 N force at an angle of 30° to the horizontal. Find the horizontal and…

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Q: Suppose the rate at which the volume in a tank decreases is proportional to the square root of the…

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Q: 2. A waterwheel with radius 7m, has 1m submerged. The wheel rotates at 6 revolutions per hour. Time…

A: waterwheel

Q: Find the value of c so that the function x² + cx if x 1 is continuous for all real numbers.

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Q: Use the Chain Rule to find dt where z = x cos y, x=t, and y = 6t²

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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: 7. Identify if the statement is Always True, Sometimes True or Never True. If lim f(x) exists, then…

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Q: Differentiate but leave your answers in unsimplified form. a) y = 5x³ 4x-² +6 c) y = √x² + 3x b) y =…

A: We know that the derivative of x^n=nx^(n-1)

Q: 7. Find the scalar equation of any plane which contains the line 7 = (3,2,-1) + t(3,-2, -1)

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Q: What is the exact value of a trigonometric function of a given angle? Select True or False for each…

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Q: -f=-9i+40j Find: -9f

A: Given vector: To find :

Q: Find the antiderivative of the given derivative. ds dt S= 13t(41²-3)³

A: Solution:-  given that now using identity

Q: Compute the surface area of the solid of revolution formed by rotating the bounded region formed…

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Q: 3. Determine vector and parametric equations of the plane with Cartesian equation 3x - 2y + z + 6 =…

A: Given equation is 3x -2y +z +6 = 0

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: Rewrite the following equation with the variables separated. y' + x + xy = yex + ex

A: Given

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

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Q: List the points in the graph in the interval -2<x< 8 at which the function is not differentiable. -2…

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Q: 15. 13. fcot³ x 9-12, evaluate the integrals. 11. ftan² x sec¹ x dx tan x sec² x dx In Exercises…

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Q: Evaluate the integral. 8 S² (4+1)" a dt √₁5 (4+10) 8. dt =

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Q: Which slope field is associated with the differential equation given below? dy dx = 1-y Choose the…

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Q: 19. F(x, y, z) = yî + xyz ĵ – 2zx k, where S is the upward-facing paraboloid z = x² + y² lying in…

A: 19) Where, S is the upward-facing paraboloid  lying in cylinder From above curves the radius of the…

Q: f = -9i+40j Find: -9f f=i-j g=12i+ 3j Find: -4f-10g u = -9i+4j Find: -5u

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

Q: Find the linearizations L(x,y,z) of the function f(x,y,z) = 6xy + yz + 7xz at (1,1,1), (1,0,0), and…

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Q: Evaluate the following indefinite integral. 1-3 Do not include the constant "+C" in your answer.…

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Q: Evaluate the integral -2 Te ex dx Note: Use an upper-case "C" for the constant of integration.

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Q: Evaluate the definite integral. WS¹ (x²-x²) dx

A: The Sum Rule:The Power Rule:

Q: Evaluate the following definite integral. Provide your answer below: Lax√812²-81 dx

A: The given integral is 8/[x sqrt(81x2-81)], limit from sqrt(2) to 2.

Q: g(x) = 4x3 - 4x + ) = (4x³. 18/5 x2 4

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Q: e (25x) lim e x→2+

A: Limx-2+ e(5/(2-x))

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

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Q: Find the inflection point given the function F(x) = f e-t² dt. No graphs.

A: Given function: To find : Inflection point of F(x)

Q: What is the limit lim x→3 √x³ - 2-5 x - 3 3 27 10 9 10 +∞ Does not exist ?

A: Given

Q: / x3 + 6x2 + 6x2 (x2 + 6x + 10)2 + + 19x – 2 dx

A: