(d) lim Use the graph of the function f to decide whether the value of the given quantity exists. If it does, find it. If it does not, enter DNE. 10- 8- 6- 2- 2. 4 6 10 -2- (a) f(1) (b) lim f(x) (c) f(5) f(x)

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

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Q: Find the Yalue + Cas

A: Using inverse trigonometric formula achieve this expression

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: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). %3D 13 r(t) = ti + t5j K(t):

A:

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

A:

Q: Determine the vector field of F. F(x, y) = 6i – 3j

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Q: 1. Let -7 3 -3 2 C = 4 A = B = -3 -3 Determine which (if any) of the following matrices are well…

A: The solution is given in the nwxt step.

Q: Find div F and curl F if F(x, y, z) = xz°i +2y°xj+62

A: Given: Fx,y,z=xz6i+2y8x2j+6z2yk

Q: Evaluate the defınite integral. 8 i + e¯´j+tk)dt 0, – (e-1 – 1) j+ k i-e'j+;k 8 (e* – 1) i – (e- –…

A: The given integral is: I=∫01e8ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: Evaluate the definite integral. i +e´j+tk )dt O e 7 – 1 e17 - (e-' – 1) + - (e~) - 1) j + k 17 O el7…

A:

Q: dg 1+sin 2x Find of g(x) dx 2x-tan 2x

A: To find the derivative of given function.

Q: If z = 52? – 3y? + 4y, find the differential dz. You should have variables dz, dy, y, and z in your…

A:

Q: Evaluate the area of the region bounded by y2 = x and y2 = 6−x.

A: To find : Area between y2=x and y2=6-x First let's find the intersection points x=6-x⇒x=3 Therefore,…

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

A:

Q: Problem 8. If the focus of a parabola is at (0, 4), and the directrix is y=-4, write the equation of…

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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)

A:

Q: (8x + 4x)v4x² + 8 – 24x³ – 32x If f(x) = (/4x2 + 8 - x*) then f'(x) = 4r2 +8

A: f(x) = (4x2 +8 - x2 )2 f'(x) = (24x2 +8 - 2x2)(8x/(24x2 +8)  -2x ) f'(x) = ((24x2 +8 - 2x2)(4x -…

Q: 1. Find fa(x, y) and fy(x, y) given f(x, y) = (csc y) Arcsin(r2).

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Q: Q2: Solve the following integrals:- (2) fd 4x2-9 xp: (3)fx sin(x +1)dx

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Q: Use the formula k(t): |r'(t) × r"(t)|| to find k(t). r(t) = ti + t°j K(t) =

A:

Q: (a) Find the value of P(?, 4) and P(?, 6) using permutation formula, where ? is the last two digits…

A: Permutation: Permutation:  The permutation is a method of arranging objects in a specific order.…

Q: Find the curvature and the radius of curvature at the point t = 0. e' cos(t), y = e' sin(t), = 3e* x…

A:

Q: by which criteria?

A: Apologies for the inconvenience. Here is the correct solution.   If a series ∑n=1∞an has either…

Q: Sy³/y² + 9dy

A: ∫ y3y2+9dyLet u=y2+9=∫u2-9u2du=∫ u4-9u2du=∫ u4du-∫ 9u2du=u55-3u3Substitute back…

Q: Q2 (a) Let n E N and let ở, w e R". Show that if ở · w = 0, then || ở + w||2 = || ||² + ||w||². (b)…

A: This question can be solved using the concept of dot product of two vectors.

Q: S 2y(yª – 4)¯³ dy

A:

Q: F'e) × r"(t)|| Use the formula x(t) = to find k(t). r(t) = 8 cos(7t)i + 8 sin(7t)j + 3tk K(t)

A: r(t)=8 cos7t i +8 sin7t j +3t kr'(t)=-56 sin7t i +56 cos7t j +3…

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

A:

Q: Describe the graph of the equation. r= -3 i+tj+(t2-1) k O Itis a parabola in the x = 3 plane, vertex…

A: This is a problem related to parametric equation plotter. Based on the x, y and z value in terms of…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: Given problem:- r(t)=cos(πt)i-ln(t)j+√(t-6)k ,t0 =7 find domain of r(t)and r(7)

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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Q: Answer the following True or False: Let f(x) be a differentiable function, such that f(– 1) = - 5…

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Q: Evaluate the following limit using Taylor series. 7 7 tan 1(x) – 7x+: lim 4x° 7 .3 7 tan (x) – 7x +…

A: Given problem:-

Q: Evaluate the definite integral. e16t i + e¬tj +t k )dt O el6 – 1 (e-- - 1) + i+ (e-1 – 1) j + , k 16…

A: To solve the given integral.

Q: Consider F and C below. F(x, y, z) = (y²z + 2xz2)i + 2xyzj + (xy² + 2x²z) k, C: x = Vt, y =t + 8, z…

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Q: Find the are lengtu of tue graph 10) of the fenetian y= x+5 over the imiterval [12, 14]. Anwens a) §…

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Q: Find V · (V × F), if F(x, y, z) = 3e*i+ 3xe"j – 8evk. - V ·(V × F)

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Q: B. Find the interval of convergence of the power series and find the sum of the series as a…

A: Series convergence

Q: The graphs of f(x) and g(x) are shown. For what values of x does f(x) = g(x)? x = -2, x = 0, x = 3…

A: We have to choose correct option

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i + 11 sin(t)j +…

A: Let's find.

Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: The function f(x) = 2x° 39x + 240x – 11 has two critical numbers. The smaller one is x = and the…

A: Topic = Derivative

Q: 15 dy dt 2-

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Q: If we apply Rolle's Theorem to the function f(x) = 2x? – 4x – 7 on the interval [ – 1, 3], how many…

A:

Q: for the N(0) is it 0k? or can I write it just k?

A: Yes, N0=-12i+12j+0k.

Q: 1. Rules of LDef nite Integrals: 12 a) b) rpx 12 12 f(x)dr 4, find the If f(z)dr = 12, " $(z)dz = 6…

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Q: rrent Attempt in Progress Find r'(t). r(t) = (tan-'(9t))i+t cos(t)j – v NOTE: Enter your answer in…

A: We have to find the derivative

Q: Practice Exercises: Find the area of the plane region bounded by the given curves 343 1. y = x² – 9…

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Q: detailed computation in determining the height of the cabin or part of the Ferris wheel at a given…

A: We are given a ferris wheel with the following informational : diameter : 64 m No of cabins : 32…