Question 28 Write the first five terms of the geometric sequence. a1 - 3; r=- O 3. 74 03 3 3 4' 16 64 256 1024 3\ 3 3 3 3, 16' 64' 256 0 3, 12, 48, 192, 768

Q: y = et + 5 is a solution to the differential equation: y' = y. Select one: O True O False

A: Given, y'=y ⇒y'-y=0

Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: Explained below

Q: limn→∞ √n = ∞

A: Given :limn→∞ n

Q: Question 2 ( Consider the function f(x)% = %3D a2+1 (a) Find the intercepts of the graph of f (if…

A: Given that      f(x) = x/(x2+1)

Q: 24 Evaluate the following. 5! 120 15 720

A: 24)  To evaluate: 5!

Q: Express the series using sigma notation 6m + 3m + 0 + (-3m) + (-6m) ...

A: Consider the series 6m + 3m + 0 + (-3m) + (-6m) ...

Q: 19. The region bounded by f(x) = -4sinx , x = n ,x = 2n, and y = 0 is rotated about the y-axis. Find…

A: This question can be solved using the concept of shell method.

Q: 3y + 2y Solving by variation of parameter y" Wronskian W is: 3e*cosx, the value of |

A:

Q: Using appropriate substitution, [sec (2x) + 1] tan(2x) dx is equal to

A:

Q: Evaluate each of the following integrals. 1. sin x cos' x dx

A:

Q: The general solution of the fourth-order differential equation y() + y" + y" =0 is: %3D y=c_1 +c_2…

A: The general solution of the fourth-order differential equation.

Q: 6. If f(x)=3x' -+ 4 + 4x +1, find f(x) and f"(x).

A: Given query is to find the Indicated derivative.

Q: -3 < x To nenen Is fox is odd ? even or

A: Use definition of odd and even .

Q: Mathematics

A:

Q: 12. Let y = 4x-4x+3. %3D (a) Find the equation of the tangent line to the graph of the function at…

A: Solve the following

Q: Find the general solution to the trigonometric equation (2 cose - 1)(tane + 1) = 0 function value,…

A: Given equation, (2cosθ - 1) (tanθ+1) = 0 To be found : general solution of given equation

Q: Given the following differential equation (E): y" + 2y' + 5y = 0. The solution of (E) is: O None of…

A:

Q: Evaluate the integral by making an appropriate change of variables.   7(x + y) ex2 − y2 dA,…

A:

Q: \n + 2, The following telescoping series ΣΗ 1 sin sin-1 n + 1 n + 2, n=1 TT converges to converges…

A:

Q: 8n + 3 E(-1) "-1. n2+3 n=1 a) Determine whether or not the series is absolutely convergent. b)…

A:

Q: 3. The polar equation r = sin(5 0) is a 5-petal rose. 3.1. This closed curve can be drawn without…

A: Given, r= sin(5theta) The graph is given by,

Q: 5.1. Find the area enclosed by r = V cos(0). (Ignore the r= 2 cos(0) for this part of the problem.)…

A: 5.1) To find the area bounded by the curve r=cosθ

Q: The following series 3 2n- 4n+1 3n n=1

A: Series

Q: 12 Indicate a general rule for the nth term of this sequence. 6m, 3m, 0, -3m, -6m, . . . a n =…

A:

Q: Find the equation of the vertical asymptote f(x) = log(x + 1) %3D > Next Question

A: Given

Q: A. Evaluate the following integrals. 1. S(Vcos x + sin x)*dx xp. 2. S cos 3x dx

A: LetI=∫cosx+sinx2dxI=∫cosx+2sinxcosx+sin2xdxApply the Sum RuleI=∫cosxdx+∫…

Q: 6. The equation 4 (x – 1)2 + 4 (y+ 2)? + 4 (z – 3)² = 1 represents a sphere. %3D 6.1. What is its…

A:

Q: 15 Evaluate. 2n - 1, where n = 6 1 32 63

A:

Q: Using appropriate substitution, sin³ (3x)cos*(3x)dx is equal to -cos"(3x) + cos"(3x) + c - cos (3x)…

A:

Q: Express the series using sigma notation 6m + 3m + 0 + (-3m) + (-6m)... E-3bn +9b E-3bn – 9b E-3bn…

A: Use the expression form the summation form

Q: Using appropriate trigonometric substitution, dx xV4 – x2 is transformed to J csc 0 de cos e do the…

A:

Q: 1. Use the graph of f(x) below to a Determine tht demain and ramge-ofthe fencion D Tind all x such…

A: From the given graph we have to find its required information.

Q: Solving by variation of parametery"-4y' + 4y = xe2x, the value of Wronskian W is: xe^4x O None of…

A: We can solve this as follows:

Q: Find the linearization of the function f(x, y) = V61 – 3x2 - 1y? at the point (4, 2). %3D L(x, y) =

A:

Q: Given the geometric sequence where a, = 2 and r = 2 Find a10-. 32 256/2 32/2 256 O O

A:

Q: Juliana invested $5,100 at 5.75% p.a. simple interest. How many days will it take for her investment…

A: Given query is to find the time taken to grow the investment to 5310.

Q: Express the limit as a definite integral on the given interval. lim 2 x;)?+9 -ах, [1,4] (x;")² + 9'…

A: Use;∫abf(x) dx =limn→∞ ∑n=1n f(xi) ∆x                       over the given interval [a, b].

Q: Without evaluating the constants, the partial fraction decomposition for 5x2 – 3 - f(x) : %3D (x³ –…

A:

Q: Find the intervals where the graph of the function f is concave up, concave down, and any inflection…

A:

Q: 4- Determine an expression for dy/dx. 3(y-2)3– x= 4x - 6.

A:

Q: If a series Σ an n=1 is convergent, then it is absolutely convergent.

A: 1)∑n=1∞ an is convergent,then the series may not be convergent.for example, an is alernating…

Q: A 17-ft ladder is leaning against a wall. The foot of this ladder is sliding away at the rate of…

A:

Q: Find an equation of the plane. The plane that passes through the point (−2, 3, 2) and contains the…

A: This question can be solved using the concept of planes in three dimensional geometry.

Q: Using the method of undetermined coefficients, a particular solution of the differential equation y"…

A:

Q: 1 The resulting 8. 6. The graph of y = log, x is horizontally stretched about the y axis by a factor…

A: Given , a graph y=log2x x is horizontally stretched about y axis by factor of 18 we need to find the…

Q: is equal to sec (2x) + In|sec(2x)|+ C sec (2x) – In|sec(2x)| + C the above the above Gsec (2x) –…

A:

Q: Find the curve length of the function 1 1. f(x) = ;x² 0 < x < 3

A: We can find the curve length as below.

Q: cos(xy) + secy = 5

A: To solve the second derivative y'' of the following function and to simplify the final…

Q: Given the following differential equation (E): y" + 2y' + 5y = 0. The solution of (E) is: O None of…

A: We have to find solution of given differential equation.

Q: Please

A: We will solve the problems.