Prove or disprove the following statement by induction 1-3-5. ... ·(2n-1) a.) 2n whenever n is a positive integer 2.4.6. •2n ... ɔ.) 1 · 1! + 2 · 2! + ...+n · n! = (n + 1)! – 1 whenever n is a positive integer

Q: Express the vector - 6i + 6j + 7k as a product of its length and direction. - 6i + 6j + 7k…

A:

Q: 3. V4- (x – 3)²dx.

A:

Q: Determine the limit: lim 4x2 x→0 sin (2x) cos(2x)

A:

Q: Could you help me with part b) also please?

A:

Q: Let i denote the square root of-1. For the two complex numbers =3e and w= 6e find 2, w. Grve your…

A:

Q: Use Simpson's rule with interval h = 1 to determine the approximate value of ở V(I + x³ )dx. Give…

A:

Q: For the points P1 (4,2,3) and P2(5,1,2), find the direction of P,P2 and the midpoint of line segment…

A: Given that coordinate of point P1 is (4,2,3) The coordinate of point P2 (5,1,2) We have to found the…

Q: S dx 2x-1 1. Vx+2

A:

Q: hey got wrong answer still

A: Here, given that: y=x4+2, x=-3, ∆x=0.01

Q: The velocity of an object moving along a line is given by v = 3t2 + 1 ft/s on the interval 0sts4. a.…

A:

Q: FEx) = 1+e siny x fCx) f'ca) = fco) = - fくb) = fCl-2) = = -15 e sin4X- se"cos4X 8 LN %3D %3D %3D…

A:

Q: Let f(x) = 2^x+ x. Find (f ^−1)′(1).

A:

Q: Question 14 Use part I of the Fundamental Theorem of Calculus to find each derivative, given the…

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

Q: The period of y = 2 sin 4x is _____. 2 pi/2 4pi

A:

Q: Find the distance between points P, and P2. Pi(0, - 3,3), Р,(8, - 4, - 2)

A:

Q: 3. Evaluate: lim X-0 \sinx 4. Using the binomial series, find the power series of f(x) =

A: We have to find the limit of a function and find the expansion of 1/x

Q: 5. y = 3x - 4 at (0. - 4)

A:

Q: A bacteria culture starts with 1,200 bacteria. Two hours later there are 1,920 bacteria. Find an…

A: A bacteria culture starts with 1,200 bacteria. Two hours later there are 1,920 bacteria. To find an…

Q: How to compare two numbers using binomial theorem. Explain step by step

A: Binomial theorem is a very powerful mathematical tool when it comes to comparing complicated…

Q: -4 Determine the limit: lim -i (и — 1)2

A:

Q: Hi for the letter (e). Isn't it supposed to be – 2 – sqrt3  and NOT – (2 – sqrt3)?? Please recheck…

A: Answer Number (e): By using tan12u=±1+cos u1-cos u, to find the exact numerical value of tan 165°.

Q: What are intervals of concavity of the function f(x) = -2x' + 6x² – 3 ? O a. Concave upward on (1,…

A: Given query is to find the the interval where function is concave upward and downward.

Q: dy 18. 0 do 2y = 0 sec 0 tan 0, 0 > 0, y(7/3) = 2

A: Given problem:- θ dy/dθ -2y=θ3 sec(θ) tan(θ) , θ>0, y(π/3) =2

Q: (i) What are the projections of the point (2, 3, 5) on the ry-, yz- and rz-planes? (ii) Write…

A:

Q: b) Performing the substitution yields the integral c) Once we integrate and substitute, the final…

A: We can solve this as follows:

Q: Differentiate exp(sec(x^2)

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

Q: Express the following vector in the form v = v,i+v2j+V3k. 3u - v if u = (4,6, – 8) and v = (2, –…

A: We can find the answer as below.

Q: Bacteria are reproducing in concentric rings in a petri dish. The circular area occupied by the…

A:

Q: Answer the following True or False. Let f(x)be a decreasing positive function. Then the right…

A: topic - area under curve

Q: Consider the function f(x) = (c) Find the intervals of concavity and the points of inflection of f.…

A:

Q: Зx+2 11. Evaluate: S -dx. x3-x2-2x Solution:

A: To evaluate: ∫3x+2x3-x2-2xdx=∫3x+2x(x2-x-2)dx=∫3x+2x(x-2)(x+1)dx

Q: fex) = I+ sinu x f(x) = 1T fcx) =-15 * sinux - secos4X %3D = -15 e sin4X- se"cos4X mL

A:

Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQUATION 1. (D^3 – 3D^2 – D + 3)y = 0

A: The given differential equation is: D3-3D2-D+3y=0 So, the auxiliary equation is: m3-3m2-m+3=0

Q: Let i denote the square root of – 1. For the two complex numbers z = 3e# and w = 6e'† find z. w.…

A: We have to find the multiplication of complex numbers.

Q: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

A:

Q: L, V4 – x²dx.

A:

Q: The following series is divergent: 3n 3n Зп — 6. - 3 — 2п | n=1 Select one: O True O False

A:

Q: Directions: Analyze and solve the following items. Show your complete solution and box your final…

A:

Q: What are the first three non-zero terms in the Maclaurin Series of f(x) = e* sin(x)? x - +-- О а.…

A:

Q: Consider the contour represented in the following figure. The points marked on the figure are А(5,…

A:

Q: ^2/sin^2(2x-6) = -1 since sinx/x =1? then limit is like x^

A:

Q: Use implicit differentiation to find dy/dx in x^2y^2 + y = x.

A:

Q: Which of the following integrals will yield In u+ C? A. SE B. S- x+1 D. S dx xdx C. S 2rdx = x+1 O…

A: From the following integrals will yield ln u+C Note:     Multiple questions are given, we are answer…

Q: 3. Evaluate: lim ( ) X-0 sinx

A:

Q: Find the first three terms of the expansion (4 – 2x). 4°(1- 폴 + 쫄 +…) O b. 2°(1 + 꼭 + 플 + …) Oc…

A:

Q: Plane travels for 9.5 hours on two-way trip between location A and B. The Plane can fly at 320 km/h…

A: Plane travels for 9.5 hours on two-way trip between location A and B. The Plane can fly at 320 km/h…

Q: 7 n³+9 3 n=1 6 n³ + 1 %3D 8.

A:

Q: A corporation manufactures candles at two locations. The cost of producing x1 units at location 1 is…

A:

Q: Can you please type it

A: Answer is given in next step.

Q: 4 x xp = Vx+9

A: