Evaluate the following: 1. S(x3+ 3x?)dx

Q: 3+ x2 ' Find the vertices of the rectangle with maximum area. Vertices = Enter your answers as a…

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Q: The graph of f'. 2+ 1- (2,0) -3 4 -3 ±1+ -2+ (-2,-3) (2,-3) 5. The graph of f', the derivative of f…

A: We have to find the value of f(5).

Q: Find div F and curl F if F(x, y, z) = 10y°2³i – 11x°z!°j – 3xy°k. „10: div F= curl F=

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Q: (5x2 – y²) dx + 2ydy = 0

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Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: Vx² +y² and A metal plug has been designed using the intersection of the two cones z = x² + y2 += 1.…

A: We have to calculate volume of plug which is intersection of two cones z=√(x2+y2) and z/3+√(x2+y2)=1…

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

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Q: Use an appropriate form of the chain rule to find the derivative. R= e5s-t. s = 80, t= ¢!/2 %3D dR…

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Q: 5- ý = 4x+3y+2 3xt2yt1

A: This is a problem of differential equation. Based on the homogeneous system of equation concept we…

Q: A certain rumor spreads through a community at the rate = 3y(1+y) , where y is the portion of the…

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Q: Verify Green's Theorem by evaluating both integrals y? dx + x² dy Ne dA ду ax for the given path. C:…

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Q: A stone is thrown vertically upwards, from the edge of a 5 m tall cliff with an initial velocity of…

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Q: Find the equation of the tangent line to the graph of y = -2x° + 6x? – 5x + 10 at the point (1,5) in…

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Q: x* +x² 5. lim,-. e* +1

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Q: In chapter 10, we will be solving system of equations. Most of the time, we solve system of linear…

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Q: What is the angle between the vectors u = and v = ? 213° O 188° O 111° 120°

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Q: Let a be a real number and f(x, y) = 3ax?y + 6xy3. Let v = 3i – j and let V f(r, y) denote the…

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Q: Find div F and curl F if F(x, y, z) = 7e*" i - 10 cos yj+ 8 sin² z k. div F=| curl F=

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Q: A tank is being filled with a liquid. Z (1), given below, is the amount of liquid in liters in the…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A: Given

Q: 6) Find the linear approximation to R(t) = VE at t=32 Use the linear approximation to approximate…

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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: (4x-3) find dy/dх y = (2х-7)6

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Q: Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North America…

A: We have to find the slope.

Q: esing pyphagoras th, Diff wt to t 2xda +rydy 20 at da dt az3 m

A: Apologies for the inconvenience.   Let, x = the distance from the wall. y = the height of the top of…

Q: 1) Find and of the following equation then simplify whenever possible. dx x = 2u* – u3 + u – 11 , y…

A: Given: x=2u4-u3+u-11, y=5u3-4u2-7u+2     As we know that; The Power rule; ddxxn=nxn-1 The Quotient…

Q: _13. If y = sin(4x – 5), then what is y'? а. у'3 сos (4x -5) b. у'- 4cos (4x — 5) c. y' = -cos (4x -…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 2. Find the area of the region bounded by y =x-1and y 3– x. Sketch the graph. Hint: Use vertical…

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Q: Evaluate the following limit: 2x2 – 3x + 5 lim x→+∞ 5x² – x + 12 - - 12 o 3 25

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Q: Write an integral that will give the area of the region in terms of dx (b) Write the integrals (do…

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Q: Evaluate F. dr. F(x, y) = 7xi + 8yj C: r(t) = ti + V4 - t²j, -2 sts 2

A: Use line integral concept

Q: Evaluate the following limit: x + 2 lim x→-3¯ x² -+ 2x – 3 O +∞ 10

A: The given limit,        limx→3-x+2x2+2x-3

Q: 4 1 T/2 Зл/2 -1 -2 -3 -4 -5 The graph of the function f(x) = cot x is given above for the interval a…

A: From the graph of f(x)=cot x, we have to find its asymptotes

Q: Find the volume of the solid that results when the region enclosed by the geviN curves. -2X ソニ e;…

A: The given curves are; y=e-2x, y=0, x=0 and x=1. So, the bounded region is as shown below. Now apply…

Q: complex form and COS U+ i sin o) be the polar form Idition and subtraction between two complex…

A: Topic:- complex number algebra

Q: Find curl (8z i + 9x j + 8y k). curl (8z i + 9x j + 8y k) = ( i )i + ( i )j + ( i )k

A: We know: Where P, Q and R correspond to the components of a given vector field:F→=Pi→+Qj→+Rk→ curl…

Q: Can you find the second subpart to this wue

A: This question has been solved completely. Please ask your query clearly.

Q: mal places as needed.)

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Q: Solve the initial value problem y′′−6y′+9y=0 for y(0)=1 and y′(0)=3. After getting the particular…

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Q: n² +1 2. Determine whether the series E 2n? +1 is convergent or divergent. If it's n=1 convergent,…

A: Given

Q: (1-) 3 4. lim

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. x + 3y2) dy

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Q: (3x-3) dx (x²-2x+1)(x²+2x+8)

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Q: Evaluate the following limits. If needed, enter INF for oo and MINF for -oo. (a) lim (Va + 3r +1-1)=…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: Describe the graph of the equation. r = - 13 i+ (1 – 12 )j + t k O It is a parabola in the plane x =…

A: Given; parametric equation    r=-13i+(1-t^2)j+tk

Q: Evaluate the improper iterated integral. x2 dy dx 1 + y2

A: Given: I=∫03∫0∞ x21+y2dydx As we know that; ∫11+x2dx=tan-1x+C And ∫a·fxdx=a·∫fxdx, where a is…

Q: Determine whether the improper integral diverges or converges. In x dx O converges O diverges…

A: Use integral test for checking the convergence of series

Q: 2Tan 'x -x 9. lim, 2x – Sin^x

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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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