Given the geometric sequence 31, 31/8,31/64 find an explicit formula for an find a7 please show work

Q: 2. Suppose z is a function of a and y and tan(V+ y) = e*. Determine dz dz and 2

A: Suppose z is a function of x and y  tan (√(x + y)) = ez^2  We have determine ∂z/∂x and ∂z/∂y

Q: y = e* – axis. and the x - axis is revolved about the y

A:

Q: iSy dx dy 3.

A:

Q: Determine a.5 tor each of the following i = (7, -3.5)andb = (-5,11. -2) b) a = (-15.13), 5 = (14,…

A: If a→ = a1 , a2 , … , an and b→ = b1 , b2 , … , bn then  a→·b→ = a1b1 + a2b2 + … + anbn

Q: 1 -dx. State whether the improper integral converges or diverges. 22 +4 Evaluate 00

A: We have to check weather the given integral is converges or diverges.

Q: 2x determine the derivative of f(x) = 3 X

A:

Q: To find two real numbers whose difference i and whose product is minimum, we can find minimum value…

A: Topic:- calculus

Q: Evaluate the indefinite integral, ſx² sinh x³ dx.

A: To evaluate: I=∫x2sinh x3dx⇒I=∫sinh x3  x2dx

Q: Find the limit 8x2+ 10x lim x0 ex-1 a. None of these. оБ. 10 1 10 d. 10 Ое. 0

A: Topic = Limits

Q: y=v16-x 2.

A: This question is based on application of integration.

Q: Solving bernoulli differential equation -2xy=2xy

A:

Q: 1. lim f(x) = -1 and f(1)DNE 2. lim f(x) = 1 and f(0) = –3 %3D %3D 3. lim f(x) = -2, 4. lim f(x) =…

A:

Q: [6]. Consider the following set of parametric equations: x = r° - 3t y = 312 – 9 On which intervals…

A:

Q: Fin d d dr

A:

Q: 6. Two triangles can be formed using the given measurements. The other measurements of the triangle…

A: For other triangle m∠B=180-55.092=124.908°m∠C=180-124.908-41=14.092

Q: 6. What type of discontinuity at x = 1 is in the function f(x) =? (A) infinite discontinuity (C)…

A:

Q: 00 Determine whether the series omverges absolutely, conditionally, or n=1 not at all.

A: The given series is ∑n=1∞-1n-1nn2+1. A series ∑n=1∞un   is absolutely convergent if ∑nun  is…

Q: 12. Evaluate: 212-3V+1 (a) (d) / sec (2) / (b) / sec (20) de dr 1 (e) rVI-1 dr dr 16+9r2 (c) sin t…

A:

Q: Find the area of the plane region bounded by the given curves: y= x, y= 2x, and x+y= 6

A: Given: y=x, y=2x and x+y=6 Now find the point of intersection between the line y=x & x+y=6…

Q: 8/16/22, 140 PM The Sine & Cosine Laws State whether the given measurements determine zero, one, or…

A:

Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…

A: Given problem:- Use differentials to estimate the amount of paint needed to apply a coat of paint…

Q: X-1 4 = = 2 – y = z 2 y-2 z-1 12 = x = -1, 3 2 Show that these are skew lines.

A: To show that the given lines are skew lines.

Q: 15. What are the coordinates of the vertices of the ellipse A. (-6,0) and (6,0) B. (0, -6) and (0,…

A: 15  y2/9 + x2/36 = 1 compare with x2/a2 + y2/b2 = 1 so a = + 6     b = + 3 so here vertices  (a,0)…

Q: For each of the following functions z, find and ду 2. z = tan-1 (2)

A: We have to find partial derivatives of z with respect to x and y

Q: y =, x = 1, x = 4, and y = 0 is revolved about the y – axis.

A: Let's find.

Q: 6. The length of a rectangular yard is measured to be 84 feet and the width to be 36 feet. If the…

A:

Q: 2x^ + xt3 dx x+ x a. In lxl+Ź In Cx t1)+ tan-"c) tc b. In \xl-Į m (x2+1)+ tan-' Cx) tc in e, wone

A: The integration of the integral is  (2x2+x+3)/(x3+x).

Q: Calculus How many numbers are relatively prime to the following number. - 209 - 323 - 867 - 31…

A:

Q: In Exercises 9 and 10, find all the trigonometric values of 0 with the given conditions. 15 9. cos 0…

A:

Q: .4 dx 2 Vx2-2

A: Given:        ∫24dxx2-2 Apply trigonometric substitution:    substitute x=2sec u and dx=2 sec u tan…

Q: The limit lim (x In( cos x-00 is an indeterminate form of type 0 0o. Select one: True False

A:

Q: az and ду az A. For each of the following functions z, find ax 1. z= sin3x cos4y 2. z = tan- (2) 3.…

A:

Q: 27. Find the magnitude of the resulting force. Round to the nearest Newton. B: 11.1 N, 111° A: 10.0…

A: Solution: Given

Q: 4. f(t) = teatcosbt

A:

Q: 10. A conical paper cup is 10 cm tall with a radius of 10 cm. The cup is being filled with water so…

A: A conical paper cup is 10 cm tall with a radius 10 cm. The cup is being filled with water so that…

Q: tan () (9) sin (4) F. Evaluate the integral r2 cos ()

A: integration

Q: dr Find de r= 3 sec 0 csc0

A:

Q: Obtain the differential equations satisfied by the given puiiicular 3. y = e5x - 3x - x2 4. y = e3x…

A:

Q: Line tangeet Find the the equetion of the Cur ve X= 2+ Sec p und at p = to

A:

Q: If f'(2) = 5 then [4f(x) – x³]x=2 %3D dx Select one: O 32 O 8 O 28 O 20 O none

A: Given f'(2)=5To find ddx[4fx-x3]x=2

Q: derivatives power series

A:

Q: Find two positive numbers whose product is 2 such that the sum of one number and the square of the…

A: Suppose, we take ?as a negative number having absolute value. Take a pair with the value much more…

Q: Expand and simplifyW – 35) · (5 + 2w)

A:

Q: cal | a*(a³ + 3)/4 dx. (+3)/4 dx. 4

A: integration

Q: Given f'(x)=-+e²2* +x² and_f (1) = +x*and f(1)=. Find f(x) 5.

A:

Q: Express the vector - 6i + 6j + 7k as a product of its length and direction. - 6i + 6j + 7k = 11 6.…

A:

Q: (ii) Prove the identity (2 - 2 cos 0) (sin 0 + sin 20 + sin 30) -(cos 40 - 1) sin 0 + sin 40 (cos 0…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: For the power series E (х-3)" find the interval of convergence. n=2 n5"

A:

Q: Question 8 Let y = tan find the differential dy of the function. O dy = e* (x² – 1) sec² \ e*"-1 dæ…

A: As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And ddxtanx=sec2xddxex=ex…

Q: 5. Let f(x) be the function f(x) = {* T*7 makes the function f(x) continuous for all real numbers.…

A: