Question 3 Find the length of the curve with the given vector equation. r(t) = (8 - 21) i+ (4 + 6t) j+ (9t-3) k, -7 sts-1 -88 -968 726 66

Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. -...

A: ln(a/b) = lna - lnb

Q: Use the appropriate limit laws and theorems to determine the limit of the sequence. 4n? + 8n +7 а, —...

A:

Q: Second-order condition for convexity. Prove that a twice differentiable function f is convex if and ...

A:

Q: Find the derivative of the function y = tan^-1 x/1-x + sec ^-1 sqrt x+1 %3D

A:

Q: 3. What is the domain of y =f°(e) # f(;)={-1°?

A:

Q: Evaluate the following limits if they exist. 1 — х — е" a) lim 2(1 — е") b) lim (1 + sin x)'/= sec x...

A:

Q: ZA So ydz + zdy+ ædz (3,4, 5) C , C2 (2,0,0) y (3,4,0)

A:

Q: The solution to the initial-value problem 4y' = -8y, y(0) = -2 %3D is y = -2e-2x Select one: O True ...

A:

Q: raluate the integral / V4x4 – 12r2 +7 xdx. A - (4x* – 12r? +7)½ + c 24 B - {(2r²– 3) /4x+– 12x²+7 – ...

A:

Q: Calculate the work done by the force F(x, y) = x3yi+ (x - y)j along the parabola y= x2 from (-2, 4) ...

A: To find the workdone

Q: 4 du Consider dx. Transforming the integrand, the result will be kJ, where k is a constant. What is ...

A:

Q: 12X dx (x+9)0

A: We know, ∫xndx= x(n+1)/(n+1) Let I= ∫12x/(x+9)⁶ dx

Q: Evaluate the following S(sec X + cot X)² dx

A:

Q: In(t+2) a. dt 4t b. For y = A sec(Ax)+ cos(sin(Ax)), find y. c. For f (x) = find f' (x) +e d. Find (...

A:

Q: a) Using an operator , solve the following differential equations d²y dy 20y = 0 dx dx2

A:

Q: 4 Consider dx. Transforming the integrand, the result will be K -, where k is a constant. What is u ...

A:

Q: Qu 4 Using an operator , solve the following differential equations d²y dy a) dx² 10 + 25y = 0 dx

A:

Q: Given: 2f(x)dx There is a function f(x) such that when u= - x°, the resulting integral is 2 du · Eva...

A: Given query is to find the the value of the indicated function.

Q: II. Find the derivative of the following functions. 1. f(x) = x3+x x4-x2+1

A:

Q: Question 3 Determine whether or not each of the following sequences is (i) bounded, (ii) monotone, a...

A:

Q: Uつ40+OLU 1ontい し いun 人 の-メS1-Xメーメを interval 3. 3. poutnd to factor p) いUtas0 -use the test -Point me...

A: Let's find.

Q: Solve the given initial-value problem. The DE is a Bernoulli equation. x² dy 2xy %3D 4y*, У(1) - dx ...

A: Topic:- differential equations

Q: 2+1 Consider f (x) = 2-2 A. Explain why the Mean Value Theorem cannot be applied to f (r) on the int...

A: Given that the function is            f(x) = (x+1)/(x-2)      

Q: d) Verify if y = 2e* + x - 1, solves y' = x - y

A: If y=2e-x+x-1, solves y'=x-y

Q: Write the first five terms of the sequence, give the exact answer: +o0 n n+ 19 J. n=1 Determine whet...

A: nn+19n=1∞  

Q: Find the equation of the tangent line to the graph of f(x)f(x) at the (x,y)(x,y)-coordinate indicate...

A:

Q: 10.fx'e'dx Task #2: Solve the following integrals of power of sine and cosine, tangent and cotangent...

A:

Q: Use sigma notation to write the Maclaurin series for the function 17 In(1 + x) k =

A:

Q: cos 2X 80 dx csc (x) sec (X) CSC

A:

Q: 10 dx. What is the appropriate formula? Given: (A) © Sa" au B 3 fa"au O Sa"au (D)

A:

Q: Evaluate the following iterated integral. 1- y² (x² + y²)° dx dy 1 0.

A: double integration changing into polar form

Q: cot 2x csc42xdr Evaluate: /2-3 cot?2x

A:

Q: Consider the differencial equation given by: 1にY01/sa) de a) This equation have Three equillibrium p...

A: (a)To find the equilibrium point. (b) Classify each equilibrium point as asymptotically stable or un...

Q: Calculate the curvature of the cycloid x(theta) = a(theta - sin(theta),       y(theta) =a(1- cos(the...

A: Question : Calculate the curvature of the cycloid x(theta) = a(theta - sin(theta),       y(theta) =a...

Q: eIn a certain Algebra class thire is q botal of 350 points Ihese points come from. s homework sets t...

A:

Q: Replace the polar equation r= with an equivalent Cartesian equation. Then identify the graph. sin 0-...

A: r=7sinθ-3cosθ       ------1 x=rcosθ y=rsinθfrom 1 rsinθ-3rcosθ=7y-3x=7y=3x+7  

Q: C_B* O UI

A:

Q: antl to determine if the sequence ne"} is strictly increasing or strictly decreasing. an Use the rat...

A: Ratio test:

Q: e) proj(a onto b)

A:

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about z = x0 and then find the nth Taylo...

A:

Q: naximum revenue, and 5. Determine the net change and the average rate of change for the function f(t...

A:

Q: Question A potato is launched vertically upward with an initial velocity of 136 ft/s from a potato g...

A:

Q: Problem 6: Solve the differential equation to find x(t) solving the initial value problem. Please be...

A: Given that the system of differential equation.first of all we find the eigen value and eigen vector...

Q: Use the formula for the binomial series: m(m-1)..(m-k+1). k! m(m-1) (1+ x)" = 1 + mx + oDx? + ... + ...

A:

Q: A triangle has vertices A (2, 3, 7), B (0, -3, 4) and C (5, 2, 4). Use vector multiplication to: a) ...

A: Given that - A triangle has vertices A (2, 3, 7), B (0, -3, 4) and C (5, 2, 4).

Q: sin 4x Given: cos?(4x) (2 – 3 sec 4x) d× what is the appropriate formula to find the integral? ® Jud...

A: Given that ∫sin4xcos24x2-3sec4xdxSolution :∫sin4xcos24x2-3sec4xdxlet, 2-3sec4x=u-3sec4xtan4x×4dx=du-...

Q: Find and sketch the domain of the function. f(x,y) = Vy-5x- 6 Find the domain of the function. Expre...

A: We have to find and sketch the domain of the function 

Q: sin(ln x) r→0+ In(sin x) Use Squeeze Theorem to evaluate lim

A:

Q: Find the volume formed by rotating the region enclosed by * = 11y and y = ¤ with y > 0 about the y-a...

A:

Q: The velocity v of a point moving along a straight line as a function of the time t [in seconds], is ...

A: