Use the graph of the function f(x) shown below to evaluate lim f(x). x 3+ 3 2 3 O 3 O 1 O DNE 2.

Q: sider the function f(x) 3x on the interval |- 2, 2]. Find the average or mean slope of the ction on…

A: Topic:-  derivatives

Q: 2 4 Find an equation of the normal line to the curve 3x¯y' – x°cos(ny) + 4x + 2 = 0 at the point…

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Q: 2. Let f(x) = vVI(2 – x). Use the local linear approximation of f(x) at xo V0.99 (1.01)². 1 to…

A: Explained below

Q: How would you evaluate |F-dr, where C is the curve with param etrizati on r(t) for astsb?

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

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Q: Consider the function f(x) = 2 – 7x², - 4 <x < 2. The absolute maximum value is and this occurs at x…

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Q: The graph of f(x) is shown (see figure). f(x) %3D Vx2 +7 Net draw o scale (a) Find the following…

A: Solution: f(x)=9xx2+7

Q: What is the area of the region bounded by the graph of r = 4 cos 0? %3D Choose two (2) correct…

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Q: The sales function for a product is given by S(x) 124 + 37.8x? – 0.6x, wherex represents thousands…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

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Q: Find the general antiderivative, F(x), for the given functions. a) f(x)=-sin? xcosx b) f(x) =/7-2x

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Q: 3. A balloon is released from the ground 100 meters from an observer. The balloon rises directly…

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Q: Use Green's theorem to evaluate F• dr. (Check the orientation of the curve before applying the…

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Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

A: We need to evaluate integral.

Q: Find volume of the solid obtained by rotating the bounded region determined by curves y = In x, y =…

A: We have to calculate volume of solid obtained by rotating the region bounded by y=lnx, y=0 and x=2.…

Q: Match the vector field with its graph. F(x, y) = yi 6. -6+ y 十H HH

A: We need to match vector field with its graph.

Q: Calculate the first eight terms of the sequence of partial sums correct to four decimal places. E…

A: We can solve as follows

Q: Solve the following differential equation step by step! y" – 2y' + y = x² + 1

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Q: (y – Jx² + y² )dx -xdy = 0, when x = v3 and y = 1

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Q: write the equation of the tangent to the Eunction: 2(x? +y=J%=25(x* -y^) at the point (3, 1) %3D

A: First we calculate the slope of tangent at the given point

Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

A: Given problem:-

Q: sheet of paper for a poster is to be 18 ft2 in area. The margins at the top and bottom are to be 9…

A: Ler the the dimensions of the sheet is  x and y in order to maximize the print area

Q: 4- part 1 Find the derivative of the function f(u) = 4u° 4 - 2u1.8 0.4 %3D = (n),1

A: Differentiate wrt u

Q: 4. Find lim (sin¬ V)cschr. r0+

A: The given limit,         limx→0+sin-1xcschx

Q: Consider a wood beam (see figure) carrying a uniform load of 20.5 kN/m (which includes the weight of…

A: answer is in next step

Q: Find the area with respect to y of the region bounded by x = y² + 2 , x = 0 , y =– 1, and y = 2. |

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Q: Problem 37: Convert the following complex numbers from rectangular form to polar form: a. 4+ j3 b.…

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Q: It is known that dx Compute . Simplify the final answer. 2х-у dx

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Q: 15. As x increases uniformly at the rate of 0.002 feet per second, at what rate is the expression (1…

A: We have given that                     ( 1+x )3= f(x)      ,  then we have to find out value of dfdt…

Q: Let S1 be the hemisphere with Cartesian equation z = 6 – /36 – x² – y? and S2 be the upper nappe of…

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Q: Find the directional derivative of f(x, y) = sin(x + 2y) at the point (-2, -3) in the direction 0 =…

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Q: A plane P, in R'is perpendicular to the vector n = (6, 2, 8), and contains the point (– 9, – 1, –…

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Q: At 10:17 a.m., you pass a police car at 55mph that is stopped on the freeway. You pass a second…

A: Here, note that the distance between two police cars is 39 miles and the time between them is…

Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: Solve the given differential equation by undetermined coefficients. y'' − 12y' + 36y = 18x + 2…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y°x²j+ 5z'yk. ,62 div F= curl F=

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Q: The curved portion of the v-t curve shown in the figure are second degree parabolas with horizontal…

A: answer is in next step

Q: For the function y=JHx +1 + Find: a) The equation of the tang ent liné at X = 2 b) The equation of…

A: Given,            y=4x+1+2xTo find : a The equation of the tangent line at x=2.                b The…

Q: 3. If dt , find g'(2). 5. g(x) =

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Q: Given | f(x)dx = 6 and | g(x)dx = 2 , evaluate 0.

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). 3 r(t) = 11 cos(4t)i+ 11 sin(4t)j+ tk K(t) =

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Q: Sheldon is being chased back-and-forth by a dog along Euclid Avenue. His directed distance (in…

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Q: sin? (x) cos (x) dx

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Q: Which type of discontinuity does the function S4- a², In x, x < 1 f(x) = 1<x < e has at x 1?

A: We need to choose correct option.

Q: 16 d :| (2V8– 1) dt da. valuate dr. dx 5.

A: We have evaluate to the given expression

Q: Describe the graph of the equation. r = (7 – 21) i + 10r j | O It is a line in 2-space through the…

A: The given equation is: r(x,y)=(7-2t)i+10tj⇒x=7-2t    y=0+10t

Q: If xy2 3x2y + C, then what is the value of C at (2,2)? %3D

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

Q: Given f(x) = 3x2 – 24x + 15, a. Write f(x) in standard form. b. What is the axis of symmetry of…

A: Given query is to write the standard form and find symmetry.

Q: Find div F and curl F if F(x, y, z) = 3y°z°i – 3x*2°j – 3xy*k. - div F= curl F=

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Q: |A:k||2||Br:||2) < ||A||F||B||F k=1

A: answer is in next step