tan (x) cos (x) 1 tan (x) +tan°(x) + C tan'(x)7tan?(x) +9]+ C 36 O 1 1 tan (x)-tan'(x) + C O sin'(x)sec?(x)7sin?(x) + 9cos?(x)] + C 63

Q: Evaluate the definite integral. (Round your answer to three decimal places.) 'In(7) to dx 1 + e2x

A:

Q: Find the average value of f over the given rectangle. f(x, y) = 2x2y, R has vertices (-5, 0), (-5,…

A: Let's find.

Q: 1. A business wants to manufacture a huge closed box with a square base a square top and rectangular…

A:

Q: x² sin 2x dx¸ Use integration by parts.

A:

Q: Evaluate the integral. 28) 335 B)- 215 A) 325 D) 36

A: Given:      ∫05  3x2 + x +6 dx

Q: x(z + 2y)100 = yz – x; Zy and xz.

A: Given problem:- x(z+2y)100 = yz-x  To find:- Zy and Xz

Q: A circle with centre C has equation x² +y² – 6x+4y+4 = 0. (a) Find (i) the coordinates of C, (ii)…

A:

Q: Consider the discrete time dynamical system 5x1 . This DTDS has 3 fixed points. Choose the correct…

A:

Q: 2x + 1 -d.x J (3x – 1) (x² + 2.x + 2)' Evaluate:

A:

Q: 5xy = 4x²z – 3yz²; yx and yz- %3D Z.

A:

Q: Determine if the equation is separable. If so, solve the initial value problem. " e'y'(t) = t (In…

A:

Q: The radius r of a sphere is increasing at a rate of 2 inches per minute. (a) Find the rate of change…

A:

Q: 2. Sketch the region and find the area of the region bounded by y = -x? + 9 and the x-axis.

A: The region is bounded by the curve y=-x2+9=-(x-0)2+9 and the x-axis.

Q: 6 If x=25eco, y=4tan8. Evaluate dy where B= Lrad Ans/-0.2647

A:

Q: x dx 24) (7x² + 3)5

A:

Q: Find the velocity and acceleration vectors in terms of u, and ug- r= 4 cos 2t and e = 5t

A:

Q: Consider / sinºx cos?x dx. |f we let u=cos x , the integrand can be transformed to A / (u²+ 2u+ +…

A: topic - indefinite integral

Q: Eind the volume of the solid genrated By hevolziay the region bounded by the curve the. line y-2at…

A:

Q: Evaluate the function. If the value is not a rational number, round your answer to three decimal…

A: We have to evaluate the function.

Q: Find the slope of the tangent line to the graph at the given point. (x² + y?32 = 4x²y, (-1, 1)…

A:

Q: 00 n +7 Use the ratio test to determine whether>. converges or diverges. 7" n=3 (a) Find the ratio…

A: To find whether the given series converges or diverges using ratio test.

Q: (1) 8 6 2 "2 -2 -4 Increasing: Decreasing: Constant: 4.

A:

Q: 1 () In solving the antiderivative of f(x) = 2 - 3sin(x) by miscellaneous substitution, the…

A:

Q: Find the derivative. (The Fundamental Theorem of Calculus -- Part 1) 19) y = cos ft dt COS-

A:

Q: 5xy = 4x?z – 3yz?; yx and yz. -

A:

Q: 3) Convert the following polar equations to rectangular equations. 1 a) r = b. r=4 4 cos 0-3 sin 0

A: (a)r=14cosθ-3sinθSince, x=r cosθ , y=r sinθso,cosθ=xr , sinθ=yrsubstitute in the given polar…

Q: S sin(2x) dx

A:

Q: 0. f"(x) = 12x; f(1) = 2 and f'(1) = -2 3. ((a)

A: Given query is to find the function.

Q: a) y=x² and y=2x+3 aJCurve accurately drown with important points lobeled b Strip is present,…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: S xdx can be solved by either algebraic subsitution or integrataion by parts. Vx- 1 A True B False

A:

Q: we the system. If the system has one unique solution, write the solution set. Otherwise, determine…

A:

Q: 14. Find the third order Taylor polynomial T3(x) of the given function at the given point. (a) S(1)…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the arc length parameter along the curve from the point where t = 0 by evaluating the integral…

A:

Q: In7 Change the Cartesian integral dx dy into an equivalent polar integral. Then evaluate the polar…

A: Put x=rcosthetha and y=rsinthetha

Q: Find any critical numbers of the function. (Enter your answers as a comma-separated list.) g(x) = x6…

A: For critical numbers, Put g'(x) = 0 and solve for x.

Q: Find the inte gral. Box Final Answer. For the definite integral, give the excact answer only dx

A: Answer is in below steps.

Q: Plot the set 1,0, on the number line. Round to the nearest tenth where applicable. Answer How to…

A: We can plot the points on the number line as below

Q: Find f'(x) and f'(c). Function Value of c f(x) = (x + 4x)(5x + 2x - 4) C= 0 %3D f'(x) = f'(c) =

A: A detailed solution is given below

Q: In²(x3) 26) dx A) 192 B) 192e3 C) 1728

A: We will use substitute method to solve the integral.

Q: Which of the points below correctly plots the point (-5, )? 12 3 4 56

A: We can answer the question as below.

Q: | æ(5")dæ

A: topic - integration by parts

Q: Given the point (-10, ) in polar coordinates, what are the Cartesian coordinates of the point?…

A:

Q: Find f'(x) and f'(C). Function Value of c x2 - 4 f(x) = C = 1 x-8 f'(x) %3D f'(c) %3D

A:

Q: Suppose i = (-3, –3, –5) and v = (-1, –5, –1). Then ů x ở is and i x ũ is

A:

Q: 2x4 +3x2 - 1 Rewrite -dx as integral of sum of partial fractions. (x3 – 4x2 + 5x)?

A:

Q: Question 8 Saved If limx→a f(x) 8(x) = 1 and limr-→a g(x) = 0 then, we must have limx→a = True False

A:

Q: Find the critical point and determine if the function is increasing or decreasing on the given…

A:

Q: If y = x + ex, find dx/dt.

A: Given query is to find the derivative of the expression.

Q: f(-1,–5)= f(-5,–1)= f(0, 0)= f(5, –5)= f(t, 2t)= f(uu, и — v)-

A:

Q: 32 2 f is continuous and | f(t) dt = 6, find the integral / t* f(t) dt.

A: Given problem:-