2. Use the limit theorems to find the following limit. x2 – 5x – 14 lim x→7 x - 7

Q: 1. 5x²+4x2-5 dx

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Q: tdt 1-t4

A: Topic = Integration

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Q: Solve tan(x)=5in the interval osxs360°,giving your solutions to 2 decimal places

A: Given,  tanx=5 x=tan-15 x=78.69°

Q: 1. The approximate value of -31.8 using linear approximation O -2.0025 O None of the choices O…

A: Ni

Q: Find div F and curl F if F(r, y, z) = xz'i+ 4y*x*j+ 62²yk. div F= curl F=

A:

Q: 2t +1 lt +8 -dt + 4t +4t 3

A: Let's find.

Q: Find the tangent plane to the equation z 5z° + 4y – y at the point (4, 2, – 66)

A: Given: z=-5x2+4y2-y      4,2,-66

Q: x² Consider the function f(x) = x² –1 (a) Find the intercepts of the graph of f (if any). (b) Find…

A: This is a problem related to function calculation. Based on the general formula and concept we will…

Q: Find V (V x F) if F(x, y, z) = 8 sin xi + 6 cos(2.x - 3y)j + 7zk. %3D | V. (V x F) =

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Q: o} (2xy+y?) dx - 2x² dy = O 2.) xy dx -(x + 2y)? dn

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Q: Find div F and curl F if F(x, y, z) = 17y*z4i – 3x°z®j – 3xy°k. - div F= curl F=

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. If it…

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Q: Find curl(6z i + 7x j+ 6y k). curl(6z i+ 7x j+ 6y k) = ( i )i + ( i )j +(i )k

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Q: 5x3+4x2-5 dx

A: Use power rule integration technique

Q: dy Given a first order differential equation dx Зx* у + tan y x' +xsec' y Q3

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Q: dx Half-angle Substitution cos x +sin x-1

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Q: Determine whether the following equation is separable. If so, solve the given initial value problem.…

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Q: Suppose z = f(x, y), where f is differentiable, a = g(t), and y = h(t). If g(3) · fy( – 2, – 6) = –…

A: Find dz/st when t=3

Q: 9) use the snell metnod to sef up end eveluete tueinteyrel tret gives the volume of the solid…

A: Using shell method, volume is evaluated.

Q: Given f(r, y) = sin(r + y) where x = s't³, y = 4s - 3t. Find f.(z(s, t), y(s, t)) = fi(z(s, t), y(s,…

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Q: 26) find the mternel of convergenu of tue power Senies (x-6)*-1 и -) 6 onsurs : aj (6,l2) d) (-6,6)…

A: A detailed solution is given below.

Q: Question 8 of 10 View Policies Current Attempt in Progress Find r'(t). r(t) = (tan(9t))i+t cos(t)j…

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Q: cion 3 of 10 plicies t Attempt in Progress curl (9z i + 10x j + 6y k). (9z i+ 10x j+ 6y k) = ( i )i…

A: Topic :- vector algebra

Q: Find V x (V x F) if F(x, y, z) = 2:xy j+ 9xyz k. V x (V × F)

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Q: x + 2y = 1 , x – 2y = 8 . Credit will be given for use of the method, and not for the so y =-7/4.

A: We will solve using cramers rule.

Q: 5. This problem will walk you through using integration to find the formula for an area of a circle:…

A: equation of circle  x^2+y^2=1 y^2=1-x^2 y=±1-x2 according to question circle lies only 1 quadrant so…

Q: dx x?(4x++9)Z

A: Integration are simplyfied..

Q: S V25 – 4x²

A: For the solution follow the next step.

Q: 2. S x²-6x-4 xp x+2

A: Given: I=∫x3-6x-4x+2dx As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫a·fxdx=a·∫fxdx

Q: Describe the graph of the equation. r = 2 cos t i- 10 sin t j + k O An ellipse in the plane x = 1,…

A: Parametric plot÷

Q: 3. Use chain rule to find given w = Vx2 +2y2 + z² and a cos (st), y = -2s In t ane 2 = 3s?Vt. 3s2Vt.

A: Follow the procedure given below.

Q: Find V. (V × F), if F(x, y, z) = 3e²*i+9xe*j – 4ev*k V· (V × F) =|

A: Use the curl and divergence for the F.

Q: FH is perpendicular to AC In the figure, AC is diameter. If EF = 3 and FG = 2. Find GH. E G EH is…

A: Similar triangles: Similar triangles are triangles with the same shape but different sizes. Similar…

Q: Find V x (V × F) if F(x,y, z) = 8xyj+ 4xyz k. V × (V × F) = (4(y+2), 4:x, 0)

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Q: 3 Consider the function g(x)= sin --1| with restricted domain [0,4]. Find and identify any relative…

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Q: Find V· (F x G), if F(x, y, z) = 11xi+j+ 4yk and G(x, y, z) = xi+ yj – zk. V· (F × G)

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Q: x-1 dx (x+1)5(x-3)5

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Q: Calculate the power series solution of the differential equation of y'- y= e* up to the five terms.…

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Q: xー1 dx (x+1) (x-3)5

A: Use substitution method for solving the  integral.

Q: sec(Inx) tan(Inx) dx

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Q: S etanx sec²x dx

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Q: dx S 9x2+16

A: We have to solve integration.

Q: Find the limit. 421 (a) lim 7+ 17 (b) lim x-0 X 3

A: Topic = Limits

Q: Change the Cartesian integral to polar coordinate | +y*)dx dy

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Q: sketch the given region R and then find its area. R is the region bounded by lines y=x, y=-x, and…

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Q: 4. x(x² – 1)² dx

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The area of the region is. (Type an exact answer, using x as needed.)

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Q: 24) use the Refio Test to determine tue canvergen ce or divergence of tue seri's 7n (~1)"(4)'…

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Q: Describe the graph of the equation. r = 14 sin 17t i – 14 cos 17t j O It is a circle of radius 14 in…

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