Q1. Evaluate the integrals below using the integral rules derived in Lectures 13-15. For each integral, you must write down the relevant integral rule and show your work in evaluating the integral. Give your answers as fractions or in terms of a. (iii) / 49-2 dx

Q: Solve the following items and show your solutions. b.) Identify if the following functions are…

A: I am attaching image so that you understand each and every step.

Q: 2pq If sin A = ,where A is an acute p2+q² • angle of a right triangle, what is sec A? p² + q? p² +…

A:

Q: sin 2x (1 - 2 cos 2x)? dx 6.

A:

Q: 'ind the exact length of the curve x = t sint y = t cos t or 0<t< 1. ou may use the following result…

A:

Q: Let a = (– 9, – 4, 1) and 6 = (10, 4, 5). Compute the projection of a onto b and the vector…

A:

Q: Evaluate using Linear Equations. v(dv/dv)=6ve"+x(2v-1) O xv-(3v²+C)elt O None of the choices O…

A:

Q: Find dx and simplify whenever possible. 1-cosh x 1. у 3D 1+cosh x 2. y = x tanh¯x + In V1 – x²

A:

Q: Evaluate by using homogeneous D.E. 3 (3x? + y) dx – 2xydy = 0 03 In(x2 + y?) + 4 = C O a = C(9x³ +…

A: To evaluate by using homogeneous D.E.33x2+y2 dx-2xy dy=0

Q: Consider the following function. f(x) = x2 – 6x %3D (a) Find the critical numbers of f. (Enter your…

A:

Q: Consider the function f(x) = x/3(x + 2)2/3 whose domain is (-∞, o). (a) Find the intervals on which…

A:

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 u · (v x w)| to determine…

A:

Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

A: Given: Here, M=2x-2y2, N=12y2-4xy. Notice that ∂N∂x=-4y=∂M∂y. So, the function is exact.

Q: 4. Solve the second order differential equation given by 2 dt2 3z = 4c", z(0) = 0, dt dr(0) 0. dt

A: We will solve the second order differential equation.

Q: dx x* +3

A:

Q: Solve the following items and show your solutions. b.) Identify if the following functions are…

A: To determine whether the given function is homogeneous or not.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Determine the horizontal asymptote of the function. If none exists, state that fact. f(x) =5 e 4x…

A: Given function is: f(x)=4e4x

Q: A solid in the formof a cube of edge 12 cm. is melted and formed into three smaller cubes of…

A:

Q: Question Using Trigonometric Substitution, evaluate: S e4*/1+ e2xdx Your answer

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 2. * S arctan x dx 1 In(x²) + C C 1. x arctan x C A x arctan x -In(x² + 1) + C -- B 1 D x arctan x…

A: Solve the given integration

Q: From a window 30 feet above the street, the angle of depression of the curb on the near side of the…

A:

Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

A:

Q: t/3 cos e sin 20 de T/6

A:

Q: Integrating Factor by Inspection: (1) y(x² + y² – 1)dx + x(x² + y² + 1)dy = 0

A:

Q: Question For the function f(x) given below, evaluate lim f(x) and lim f(x). X→ー0 2x4 +3x +2 f(x) =…

A:

Q: 1. cot? 2x csc* 2x dx

A:

Q: dx Assume that x= x(t) and y= y(t). Let y =x +4 and -5 when x= 1. dt dy Find when x= 1. dt

A:

Q: VECTOR DIFFERENTIATION: If R = e^(−t) i + ln(t^2+ 1) j - tant k. Find: (a) dR/dt, (b)…

A: R=e-ti+ln(t2+1) j-tant k

Q: What is the value of the trigonometric expression below? * sin 0° + sin 1° + sin 2º + sin 3º + ... +…

A:

Q: Integral Calculus: Integration by Parts (Original method

A:

Q: What is the magnitude of the vector cos 0 i + sin 0j+ 1? 01 O2

A:

Q: (i) re dr -2

A:

Q: *** . ***** ******* . Determine whether the lines intersect, and if so, find the point of…

A: To find the point of intersection of given lines.

Q: - Find the Taylor series expansion for the given function about x =g. :- Using the Taylor series…

A:

Q: The value of p for the series En=1n! e¯n by using ratio test is 2 O 8.

A: Ratio Test: Let ∑n=1∞un be a given series such that limn→∞un+1un=ρ Then the series converges iff…

Q: 1 EVA LUATE ECs) OF THE DIFF ARD 4(0)-0. dy dt² dt

A:

Q: 70 11 odometer. To find out how long this road is, you record the car's velocity at 10-second…

A: To find the length of the road, given velocity

Q: Q2. Evaluate the integrals below by first using trigonometric identities to simplify the in-…

A: We have to find value of given definite integral.

Q: Find an equation of the plane with the given characteristics. The plane contains the y-axis and…

A: Plane in 3D: The equation of a plane in 3D is ax+by+cz=d If by is removed, the graph of the…

Q: tan x dx sec x+4 cosx 5.

A:

Q: dx

A:

Q: Solve the following items and show your solutions. c.) Find the general solution and solve for the…

A:

Q: Find the centroid of the solid generated by revolving the region about the indicated axis the area…

A: There is more than 1 question, as per the Q&amp;A guidelines, We are answering the 1st question. If…

Q: Find the Laplace Transform of the following functions s? – o? 1) f(t) =t cos(@t) Ans. F(s)= (s² + w*…

A: According to our guidelines, we can answer only three subparts of a question. Kindly repost the…

Q: S e2x sin 2xdx

A:

Q: Use the position function s(t) --4.9+ 650, which gives the height (in meters) of an object that has…

A:

Q: Determine whether the planes are parallel, orthogonal, or neither. 4x – 20y – 4z = 4 3x – 15y – 3z =…

A:

Q: What is the lateral area of a cylinder with a height of 7 cmand diameter of 240 mm? 3360π cm2 1680п…

A:

Q: Question Use the First Derivative Test to find the location of all local extrema for the function…

A:

Q: Consider the function y = 5cos(x). What are the exact values of C in the interval [0, 2pi] such that…

A: