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

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

A:

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

A: Vector

Q: Vcsc² 0 – 1d0 [In (sin 0)]² + 23

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Q: Evaluate the limit 11г3 — 7? — 9х lim 10— 5х — 5а3 I+ 00

A: This question can be solved using the concept of limits.

Q: 5x3+4x2-5 dx

A: Use power rule integration technique

Q: Evaluate the definite integral. i+e'j+t k )dt ell (e-l – 1) + (ell – 1) i – (e-1 – 1) j +, k 11 ell…

A: Given: I=∫01e11t i+e-t j+t kdt   As we know that; The Power rule: ∫xndx=xn+1n+1+C And…

Q: Use the formula r(t) = |r(t) × r"(t)|l| ||r(t)||³ to find k(t). %3D r(t) = t’i + t3j K(t)

A: r(t)=t^2i+t^(13)j r'(t)=d(t^2i+t^(13)j)dt=2ti+13t^12j r''(t)=d(r'(t))dt=2(1)i+13×(12t^11)j…

Q: Зx* у + tan y dy Given a first order differential equation dx x³ +x sec? y (a) Clarify the exactness…

A: To solve the given differential equation

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

A:

Q: sin() cos( 2

A: To Find :   ∫sinx2cos3x2dx   Note: 2sinAcosB=sin(A+B)+sin(A-B)

Q: 4- to --6 -5 -4 -3 -2 -1 5- ver which interval of z values is f'> 0? о (2, о) O 12, 0) 0(- 00, 2)…

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Q: Describe the graph of the equation. r = 7 cos t i - 16 sin i j+k O An ellipse in the planex = 1,…

A: We have to describe the graph of the equation.

Q: short

A: Please refer to the image below

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

A: This question can be solved using the concept of domain and of functions and value of a function at…

Q: d d Calculate r1(t) · r2(t)] and dt ri(t) × r2(t)] first by differentiating dt the product directly…

A:

Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function F(x) = x…

A: A complete solution is given below.

Q: sec(Inx) tan(Inx) dx

A:

Q: The following series is divergent: (8")(10") (7")(9")+1' n=1 Select one: O True O False

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Q: elin (sin x+ cos x) dx 1. S ecosx

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Evaluate the definite integral. e12' i + e¯*j+tk )dt e12 – 1 1 (e- – 1) + 12 O el2 – 1 e12 -i - (e-…

A: Integral

Q: QI: Find dyldx for the following functions:- (3) y = (tan x)tnz+ t (4) y = sin-(x² +x) + 5" %3D

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Q: Determine the vector field of F. F(1, y) = 9i – 3j

A: kindly attached following graph.

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

A:

Q: Q2/A) Find the particular solution for the following D.E., the boundary condition is (y-0@x

A: The given equation is dy=ex-ydx.

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 the arc length of the curve y = from x=2 to x=3 2x2 16

A: Use arc length formula

Q: Cosx dx Vi+sinx

A: Given :∫cosx1+sinxdx

Q: Evaluate the limit using L'Hospital's rule ez – 1 lim z+0 sin(82)

A: Here I have appended the formula used in the solution part.

Q: y = Vx + 3 from x=1 to x=4

A: We find the area under given curve and bounded by axis and given lines x=1 & x=4 using definite…

Q: For ​f(x)=x+5 and ​g(x)=3x+1​, find the following functions.   a. (f◦g)(x)​; b. (g◦f)(x)​; c.…

A: Topic = Functions

Q: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

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 the general solution of the given variable separable egm atim. dy *+ ay? (2) %3D

A: Given :dydx=e3x2+4y2

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

A:

Q: 1- x2 If f(x) = then f'(x) = x² + 1 2/x(x² + 1)³

A: Given : f(x)=xx2+1   To Show: f'(x)=1-x22x(x2+1)3

Q: Consider the function f(x)=−3x2+30x−2.   a.   ​Determine, without​ graphing, whether the function…

A: Given; f(x)=-3x^2+30x-2

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: 8. Describe the steps you would use to determine the absolute extrema of the function Ax) = (x- 3)e"…

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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: Q2: Solve the following integrals:- (1) fx² sin x dx (2) f dx 4x2- xp: (3)f x sin(x + 1)dx

A:

Q: a) Determine whether the series 11n? + 8n + 32 is n³ + 3n2 – 7n + 1 n=1 RY convergent or divergent.

A: Since you have posted multiple questions which are not interlinked i can do first question as per…

Q: A ball is thrown into the air and its position is given by h(t) = - 4.3t2 + 41t + 15 where h is the…

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Q: 11. Let -4 А -4 -4 -3 -3 (a) (i) Show that -4 is an eigenvalue of A with corresponding eigenvector…

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines.

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: Find the equation of each normal of the function f(x) = 1/3x^3 + x^2 + x - 1/3 which is parallel to…

A:

Q: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: (D² +1)y = sec x. %3D

A:

Q: r(t) = (tan(5t))i+t cos(t)j – Vtk

A: Given: rt=tan-15ti+tcostj-tk