Find the gradient of the function at the given point. f(x, y) = 3x + 4y2 + 10, (3, 4) ∇f(3, 4) =

Q: Question 1: 2nd Order ODE, Homogenous. Find the general solution, and the values of the given…

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Q: Sx*e-2x dx e-2 (2x* + 4x³ + 6x² + 6x + 3) + C 4 A e-2x (2x* + 4x3 + 6x² + 6x + 3) + C B -2x 3 x*…

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A: LetI=∫cos5xcos3xdxI=12∫2cos5xcos3xdxWe know…

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A: Given problem:- (a) Find an equation of the tangent plane to the surface at the given point.     z =…

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Q: Find the 2 possible pairs of polar coordinates for the following rectangular coordinates. а) (-5, 0)…

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Q: Use the root test to determine whether >a, converges, where An is as follows. n=1 332. a, = n/ e"

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A: Given query is to find the distance traveled by the body

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A: In this question we will use basic concepts of calculus i.e concepts of volume of solid revolving…

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A: 1) f(x)=2x3-1 at (1,1) 2)f(x)=g(u) and g(u)=u(x).

Q: | cos(Vx) dx A 2 Vx sin (Vx) - 2 cos ( Vx) + C C 2 Vx sin x (Vx) - 2 cos (Vx) + C B 2 Vx sin (Vx) +…

A: To evaluate: I=∫cos xdx Substitute x=u⇒12xdx=du⇒dx=2udu So, I=∫cos u 2u du=2∫u cos u du

Q: Find the area bounded by the graphs of f(x)=x+2, g(x)=3x²+5 , x=-1 and x=1.

A: Explanation of the answer is as follows

Q: * | 2x)cx csch (2 sin -1 V1-4x²

A: The given integral,       ∫csch2sin-12xdx1-4x2

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A: Let's find.

Q: Find Duf at P. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = 2 ¿i + k - Duf i

A: Given that       f(x,y,z) = 6x5y3z4 ; P(1,-2,1); u=(1/3)I+(2/3)j-(2/3)k  Here we have to find Duf at…

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Q: Evaluate/Find the following integrals. 2 4. S2-3 3 -dy 1 У +у 2

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Q: sketch the graph of the rational function with the following properties: touches the x axis at 3,…

A: A rational function has following properties,touches the x axis at 3crosses the x axis at -2vertical…

Q: pon homogencous Lincar ODE y'+3y = 18x² yro)=-3 y'@)=0 And exace sol'n 5.

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Q: 3 -5 6. Evaluate the determinant for the following matrix: 1 O A. 8 О В. -2 О С. 5 O D. -4

A: Solving the problem by finding the value of the determinant.

Q: S 4x* sin2x dx A (2xª + 6x² + 3) cos 2x + (4x³ + 6x) sin 2x + C C (2xª – 6x² • 3) cos 2x + (4x³ –…

A: Integrating by parts : ∫u.v dx =u∫v dx -∫dudx∫v dxdx dxndx=nxn-1 ∫cos(ax)dx =1asin(ax)+C ∫sin(ax)dx…

Q: SEATWORK Solve two problems; one problem from #1 and one problem from #2. Submit clear and upright…

A: Since you have posted multiple questions i can do first question with first three subparts as per…

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A: Here ,we have given a definite integral.Now we solve it by using rules of integration. Then we put…

Q: Find the area in square units bounded 1) y2 = 4x, x=0 to x= 4

A: Area Bounded by the curves :   If x=f(y) and x= g(y) be two continuous function on a,b and f(y)…

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Q: indefinite integrals: Show complete and detailed solutions. Express your answers in simplest form…

A: Product Rule of integration : ∫u.v dx =u.∫vdx -∫dudx∫v dxdx ∫yn dy =yn+1n+1+C ∫cosu du =sin(u) +C

Q: Which of the following is the correct definition of the limit? The lim f(x) = A, if and only if, for…

A: Explanation of the answer is as follows

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Y1 = x² + 2x + 1 Y2 = 2x + 26 dx y2 35 30- 25 20- y 15 10

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Q: Find an equation of the plane that passes through the point P(3, 5, 1) and has the vector n = (1, 8,…

A: As we know that; The equation of the plane which is passing through a point Px0,y0,z0 and a normal…

Q: Evaluate |//.(a (x + y – 5z) dV where E = {(r, y, z) | - 4< y< 0,0 < I < y,0 < z < ¤ + y³} E Round…

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Q: Use seperation of variable to solve the following differential equation (DE): (11 + x) dy – y dx = 0…

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Q: Consider the following problem. Find the distance traveled in 15 seconds by an object traveling at a…

A: answer is in next step

Q: (a) Find an equation of the tangent plane to the surface at the given point. x + y + z = 10, (3, 3,…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: (cos x+xcost)dt +(sint – t sin x)dx = 0 Ans. t cos x+x sint = c

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Q: Find the directional derivative of f(x, y, z) = 5y at P(5, 1, –4) x + z in the direction from P to…

A: We have to find directional derivatives for the given function.

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

A: We need to minimize f(x,y,z).

Q: (k) (In n)n n> 2.

A: k. 1ln nn ,  n≥2let, un=1ln nnun=1ln nn12=1ln nn2by cauchy roots testlimn→∞  un1n=limn→∞  1ln…

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-8, 0,…

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Q: x³3-* dx -x³3-*In (3) + 3x² 3¬× ln²(3) – 6x 3¬×ln³ (3) + 6 3¬× In*(3) + C A B -x³3¯* ln(3) + 3x² 3¯*…

A: Let's find.