Find an equation of the sphere with center (-3, 2, 7) and radius 7. (x+3)² + (y-2)² + (z-7)²=7² What is the intersection of this sphere with the yz-plane? I X = 0

Q: Given that the function f(x)=x²-2x+1 İS continuous on [0,2] and differentiable on (0,2), which of…

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Q: Evaluate x +4 lim₂+−1+ f(x) if f(x) = { -x+1 x -1

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Q: (1)=2x+5 y(2)=x^2-8x+17   1. find the value of y(2) at its minimum, and the rate of change of…

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Q: - Given the points A: (0,6,2) and B: (-5,-4,6), find the vector u AB

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Q: Gabby is using a rental agent in order to rent an apartment for college. She would pay the agent a…

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Q: . The symmetric equation of the line that passes through the points (3,0, 11) and (2,6,7

A: We have to find the symmetric equation of the line that passes through the points (3, 0, 11) and (2,…

Q: Find the unit tangent vector at the indicated point of the vector function T(A/2) = ( r(t) = et…

A: Given vector r( t ) = e6tcost i + e6tsint j + e6t  k

Q: Consider the vector function r(t) = (t, t¹, t8) Compute r' (t) = ( T(1) = ( r"(t) = ( r(t) xr' (t) =…

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Q: Evaluate lim h→0 1 2 5 (x+h) ² 2h 1 5x²

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Q: Find an equation of the sphere that passes through the origin and whose center is (−2,1,3) Be sure…

A: Given that the sphere passes through the origin and whose center is (-2,1,3).

Q: What is S² S 2 9. b. C. k|x EN d. = www 2 sin 0 1 r cos² 0 drd0?

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Q: Suppose the total cost C(x) (in dollars) to manufacture a quantity x of weed killer (in hundreds of…

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Q: X√ хр. т-х а- by substitution b. by integral by parts

A: Topic:- application of integration

Q: 1. Establish the convergence of the series given by n=1 If the series is convergent, find the sum. 2…

A: Given series is ∑n=1∞2(3n+2)(3n-1)

Q: (x) = cos² (5 — x), then ƒ' (0) = -2 sin(5) -6 sin 5 2 cos(5) sin(5) -2 sin(5) cos(5)

A: Topic:- derivatives

Q: For the function, find the following. f(x) = 7√x5 (a) f'(x) (b) F"(x) (c) F"(x) (d) (4) (x)

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Q: The vector field F(x,y) = (5y + 3x)i + (3x + 5y)j is not conservative. Select one: O True O False

A: Let the vector field is F(x,y) = M(x,y) i + N(x,y) j   Then, this vector field is conservative if we…

Q: Step 1 To find the x-intercept, set y = 0 in the equation 3x - y - 9 = 0, and then solve for x. 3x -…

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Q: A painting is purchased as an investment for $175. If its value increases continuously so that it…

A: A painting is purchased as an investment for $175.If its value increases continuously so that it…

Q: Find f'(x) if f(x) = O (x²-5x) (3x²+29x-35) (6x+7)* O(x²-5x) (2x-5) 9(6x+7)² O(x²-5x) (-3x²+27x+14)…

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Q: 7. Find the surface area generated by revolving y = x² from x = 0 to x 2 about the x-axis. = a.…

A: To find the surface area generated by revolving y=x2 from x=0 to x=2 about the  x-axis.

Q: Verify the following identities 2c05¹ √√x=cos (2x-1) 0<x<1

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Q: Graph the rational function. f(x) = 2x+2 x+4

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Q: Find the distance between the point and the line given by the set of parametric equations. (Round…

A: Please see the below picture for detailed solution.

Q: 4. Find the equation of the plane that contains both the lines L₁ and L2 whose parametric equations…

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Q: Step 1 To find the x-intercept, set y = 0 in the equation 3x - y - 9 = 0, and then solve for x. 3x…

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Q: Find the derivative of the following -→7 Fcx) = sin-¹ (In x)

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Q: Find sin 2x, cos 2x, and tan 2x if sin x = √5 and x terminates in quadrant

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Q: Find the required higher derivative. Show your complete solution. 11. x=a²bsin 2at y=ab² cos 2at ;…

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Q: The function f(x) = except when x=2 3x²-5x-2 x²-7x+10 except at x=2 and x=5 = 3/3/201 O except at…

A: given  f(x)=3x2-5x-2x2-7x+10for continuous x2-7x+10≠0

Q: Find y' if 8√√xy + 6x = 3y. 4y+ 6√√xy+4x 3√xy O 3√√xy-4y 4x 4x-3√√xy 6√√xy+4y 4y+6√/ay 3.√√xy-4x O…

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Q: Find the vector and parametric equations for the line through the point P(-1, 0, 2) and parallel to…

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Q: (12) f² f(x) dx The following is the graph of f(x)=√4x². Determine (A) tan-¹(2) - tan-¹(0) (B) (C) π…

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Q: 0 Find the derivative of the vector function r' (t) = ( r(t) = ln(12-2)i + √5 +tj+4e²¹ k

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Q: Find f" (x) if f (x) = tan(x² − 1). ○ 2 sec² (x² - 1) ○ 2 sec² (x² − 1) (1 + 4x² tan(x² − 1)) ○ 2…

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Q: whats the distance of JK, where J(4,3) and K(2,-3)?

A: Concept Let two points  P( x1 , y1 ) &amp; Q( x2 , y2 ) Then PQ = ( x2 - x1 )2 + ( y2 - y1 )2

Q: Example 1 Find the function f(x) satisfying the given conditions: f'(x) = 2x + 4, f(1) = 3.

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Q: x f(x) g(x) g'(x) -3 10 -5 -2 10 -3≤x≤-2 positive negative negative positive -2 0 -3 -2 0 The…

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Q: State whether the following is true or false by differentiation. 1 [cos²(x) dx = x + ¹/ sin(2x) + C…

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Q: Can we apply L'Hôpital's Rule for: lim O a. Yes O b. TBH, I don't know. O c. No O d. Maybe. x -?…

A: let  I=limx→0(x4e4x)we know  e0=1

Q: 1. The amount of pollution in a certain a certain lake is P(t)= (tª + 3)³, where t is measured in…

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Q: (π/2, π), (π, 3π/2), and (3π/2, 2π). Which two are possible, and why? D. If is a real number on the…

A: we wil find the required.

Q: What is the volume of solid generated when area bounded by y=x, y-axis and y=2 is revolved about…

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Q: F(x) = ²* e² a point with x-coordinate 2. (a) Let dt. Find an equation of the tangent line to the…

A: Let's find equation of tangent line.

Q: (c) (d) y² + 4y = cos2x y' +9y=e'; y(0) = 0, y'(0)=4

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Q: Congress is debating a proposed law to reduce tax rates. If the current tax rate is r%, then the…

A: Answer is in step 2.

Q: FIND THE SOLUTION TO THE FOLLOWING DE. 5. y"" - 3y" + 3y' - y = 4 + 3xe*

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Q: Find the distance from the point (1, −3, 6) to the x-axis.

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Q: 6. In finding the centroid of the area bounded by y=x, y-axis and y=2, which of the following gives…

A: In finding the centroid of the area bounded by y=x, y-axis and y=2, to determine the moment about…

Q: The company FeOre is specialized in making rectangular flower boxes with a volume of 0.8 m³. The…

A: we need to find the minimal cost