Evaluate the following limit using Taylor series. 7 7 tan 1(x) – 7x+: lim 4x° 7 .3 7 tan (x) – 7x + 3* lim (Simplify your answer.) 4x5

Q: 12 For the given function y 3 cos ( 0 2 state the following (show al Work) a) Amplitude b) Period c)…

A:

Q: 15 of 20 -722 –8x =? limz→00 3–72²+6x+6 O Does not exist O 00 O 7

A:

Q: 2. S(e" + e-3)² dt

A:

Q: Given the equation z + 10z°y – 8y² + z* = 4 az Use implicit differentiation to find dz

A:

Q: Find the volume of the solid Formed by revolving the region bounded by the graphs OF y=x +1, y = 0,…

A: Find your answer below

Q: 11. Rules of Definite Integrals: If f(x)dx =12, S" S(x)dx = 6, and "S(x)dx= 4 , find the following:…

A: We need to perform integral.

Q: your

A: Please refer to the image below

Q: Consider h(x, Y, z) = cos (xy) + eY% + ln (xz). Determine the directional derivative of h at the…

A:

Q: 2. fx Arctan xdx

A:

Q: Suppose a certain baseball diamond is a square 90 feet on a side. The pitching rubber is located…

A:

Q: Use the formula k(t) ||r(t) × r"(t)|| to find «(t). %3D r(t) = t²i + t°j K(t)

A: We have to find the value of k(t).

Q: In x

A: A detailed solution is given below

Q: (tan x) dx

A: Given query is to find the integral.

Q: Represent the plane curve by a vector-valued function. x2 + y2 = 16 r(t)

A: The given plane curve is   x2+y2 =16.  We have to represent the curve by a vector valued function…

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…

A:

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: Find r'(t). r(t) = (tan-'(11t))i+t cos(t)j – Vfk NOTE: Enter your answer in terms of i, j, and k.…

A:

Q: If y = x2 is expressed with parametric equations such that = 6 when x = 1, what is ? dt dx %3D dt

A:

Q: sec(Inx) tan(Inx) dx

A:

Q: Match the equation with its graph. x2 y2 z2 + = 1 9 9 16 4 -5

A:

Q: Suppose that f(z, y) = z*y°. The directional derivative of f(1, y) in the directional ( – 1, – 2)…

A: We can solve this as follows:

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) = 9e*Y i – 8 cos yj+ 4 sin? z k. %3D div F= curl F=

A: F(x,y,z)=9e^(xy)i-8cosyj+4sin^2zk ∇F=∂F(x,y,z)∂xi+∂F(x,y,z)∂yj+∂F(x,y,z)∂zk…

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

A: Given a vector function

Q: Integration

A: We will solve the integral.

Q: Find r'(t). r(t) = (tan-'(9t))i+t cos(t)j – Vēk NOTE: Enter your answer in terms of i, j, and k.…

A: We can solve this as follows:

Q: dr2, dri r(t) - r2(t)] = r1(t) - r2(t) and dt dt dt dro dr.

A:

Q: Q2) Find the integral of: L*„6 tan*x dx 4

A: LetI=∫-π4π46tan4xdxTake the constant…

Q: COSX sin x dx 4. S 1-ఆశి అరికి న

A:

Q: For the following telescoping series, find a formula for the nth term of the sequence of partial…

A: Write the nth term and  add them to get Sn .

Q: For x = t3 + 2, y = 3 – t, give an equation in terms of x and y.

A:

Q: d 27. dx ], cos t dt

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Please answer all parts in detail.

A:

Q: B. Find the area bounded by the curves, the axis and the given values of y. Sketch the graph. 4.…

A:

Q: Find V x (V x F) if F(x, y, z) = 5xyj+7xyz k. %3D V × (V × F)

A: Curl vector

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

A:

Q: dw given w = a2 + 2y2 + 22 and a = cos (st), y = -2s Int and Use chain rule to find 2 = 3s' Vi.

A:

Q: Use the given function value and the trigonometric identities to find the exact value of each…

A:

Q: S2 2 sin?x cos5x dx =?

A:

Q: x+1 8. -dx (x-1)

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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

A:

Q: 1. Let -1 -5] 3 -7 3 -6 -3 A = B= 6. 5 -3 -2 4 2 | -3 Determine which (if any) of the following…

A:

Q: (D2 – 1)y = 2e-*(1+e-2*)-2, %3D

A:

Q: dx 5-x?

A: We will solve the integral.

Q: 15 dy dt 2-

A:

Q: sec(0) = cot(0) = (b) y (1, -1) sin(0) = cos(0) = tan(0) = csc(0) = sec(0) = cot(0) =

A:

Q: dy tay +x?

A:

Q: Find div F and curl F if F(c, y, z) = 9e®Y i – 8 cos yj+ 4 sin? z k. div F= 9 y eY + 8 sin(y)+4…

A:

Q: Find both first partial derivatives. Z = cos(4xy) %3D Oz %3D ду

A:

Q: Find the series radius and interval of convergence for what values of x does the series converge x"…

A: We need to find radius and interval of convergence.