(sin x + cos x)dx sin² x sin 2x sec x dx sin 2x dx 2 sin x cos² x

Q: . a. Approximate y = e# using the Taylor polynomial P3 (æ) of y = e at 0. а.

A: taylor polynimial formula and steps I given below.

Q: The functions f and g are continuous and differentiable with f'(x) = g(x). Selected values of the…

A:

Q: Suppose we have f (x, y) = x + 1' What is the level curve for f (x, y) = 5 ? (a) a parabola (b) a…

A: Let's find.

Q: 2) Choose one of the following options, which interprets best the area under f(x) on the interval 12…

A:

Q: 2Tx [e?n* + 23c] dx

A:

Q: Learning Task 2: Expand each function (using the appropriate technique/ formula). Compute the…

A:

Q: 34. f (г) — 1 ; с34

A:

Q: (x² + 8y²)dx – 6xydy = 0

A:

Q: g(x)=arcsec(4e^x) Find the derivative

A: Find the derivative of the function.      g(x)=sec-14ex

Q: Convert from rectangular to spherical coordinates. (Use symbolic notation and fractions where…

A:

Q: Evaluate the directional derivative Duf (2, 3) if ƒ (x, y) = and u is the unit vector in the same…

A: Given problem:- Evaluate the directional derivative Duf(2, 3) if f(x, y) = x/(x2 - y) and u is the…

Q: 3. Express the following integral as a one-dimensional integral in term of r, where E is the region…

A:

Q: 12. f (x) = xe -x

A:

Q: 2. Y= 2 Arccos (1-5+ V4x – x²

A: Let's find.

Q: (a) A function f (x) is given as 1 x0 2x Evaluate lim f(x) numerically by constructing a table. (b)…

A:

Q: If f is a one-to-one function with f(3) = 6 and f'(3) = 4, what is the value of (f') (6)? (1)'(6) =…

A:

Q: Question 1 -x2 1 4a?t prove that VE If v = dv ôt

A:

Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

A:

Q: Consider the following planes. Sx+ 6y -2= 66 x- 12y + 22 0 (a) Find the angle between the two…

A:

Q: Evaluate this path limit: 4.ry3 lim (z, y)¬(0, 0) 2x² + y6 I=y% =???

A: To find: Limit of the function of two variable along the given path.

Q: Evaluate the following limits analytically, if it exists. (a) Vx+14 – 1 lim x→-10 2x (b) 5x +7x lim…

A: Given problem:-

Q: ind the total area of the shaded region shown to e right given by the curve 3D2(sin x)/1+ cos x. -2…

A: Given query is to find the area of the region.

Q: 3x+4x-2x+8 a) h(x)= b) g(x)= 5x" – 3x + 12x² +1 x*-16 HA HA VA VA SA SA 2x +7x-11 2-9 2x'-x + x-1 c)…

A: We have to use properties of asymptote to solve the problem

Q: Express the repeating decimal as the ratio of two integers. 0.02 = 0.0222.. The ratio that…

A:

Q: 6. Use parametric differentiation to find if x= 212 +2, y=t* -7 dx Solution:

A:

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -12, 6), and the plane given…

A: Given

Q: A particle is moving along graph paper in a magnetic field. The intensity of the field at the point…

A: The intensity of field will show steepest descent in the direction opposite to the gradient…

Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Determine whether the planes are parallel, orthogonal, or neither. бх — 5y + z %3D4 x + 2y + 4z = 1…

A:

Q: Find the average value of f(x) = over the interval [1, %3D (2x2 + 1)? Enter the exact answer.

A: Given:f(x)=x2x2+12    a=[1,3]

Q: . Y= In (- (x-2)2

A: To solve the second derivative of the function

Q: The base of a three-dimensional figure is bound by the x-axis and the curve y = e on the interval…

A:

Q: 5.SUPPOSE tu at fex)= XJgcK)· If 903)=16 and g C3)=-5.what is f'(3)?

A:

Q: Given the vectors, ū = -3i+2j and = 4i – j, find 4ü-27. %3D (-20,10) (20,-10) (-20,-10) (20,10)

A:

Q: Directions: In implicit differentiation, we differentiate each side of an equation with two…

A: according to company rules we can answer only first question and rest can be reposted.

Q: 4. f(x) = sin xand g(x) = 2x 5. f(x) = x² + cosx and g(x) = 3x + 4 Guide Questions: 1. How did you…

A:

Q: Use the series approximation to evaluate the integral to within 0.0001. (Answer with 5 decimals.)…

A: Let's find.

Q: dy dx 1+8sin ?x 1 Given tan(3y)=3 tan x . Show clearly that

A: As we know that; The chain rule: fgx'=f'gx·g'x   The trigonometric identities; 1). tanx=sinxcosx 2).…

Q: A particle travels along the x-axis such that its velocity is given by v(t) = = t.9 sin (3t). What…

A:

Q: Match the polar equations with the correct polar curve. (i) r = 2 cos (0), 0 <o <T/2. --- (ii) ----…

A:

Q: For what values of k does the following system has a solution? x – 3y = 6 - x + 3z = -3 2.x + ky +…

A:

Q: Ja (2) Suppose that F'(x) = f(x). What is the integral from a to b of f(x), with respect to x?

A:

Q: Determine whether u and v are orthogonal, parallel, or neither. u = (cos(0), sin(0), 9) v = (sin(0),…

A:

Q: Evaluate the following rational function with the following (a, b, c, and d). 5+3x*+4x3-13x2+13x-1…

A: Let's find.

Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis.…

A:

Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D0.

A:

Q: 6. (6x – 3y + 2) dx - ( 2x - y– 1) dy = 0 ans. 3x - y + C = 5 In | 2x - y + 4|

A:

Q: For the functionf(x) given below, evaluate lim f(x) and lim f(). X-00 X→ー0 f(x) = –18x (x – 1) (x +…

A:

Q: k(а-2)+ k(5а) B- If k(a) = -43a+2, find 3

A: The objective of the question is evaluate the value .

Q: Let Z1 -2V3 – 2i and z2 = -1 + iV3 • Z2 Find the product: z1 • Z2

A: To find the product of the given complex numbers.