(1) (2) (4) B" A" A" B" 90 B'

Q: Σ nº +1 n=1 aluate the following integral. (If th dx x9 +

A:

Q: Question 2 ( x? Consider the function f(x) = . x2 -1 (a) Find the intercepts of the graph of f (if…

A:

Q: limn→∞ √n = ∞

A: Given :limn→∞ n

Q: Express the limit as a definite integral on the given interval. -Дх, [1,4] (x;)2 + 9 lim i = 1 dx

A:

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

A:

Q: For which of the following series is the Ratio Test inconclusive? Select one: Σ Σ * (-3)* +1 n=1…

A: To find for which series the Ratio test is inconclusive.

Q: 3n4 4n – 1 n=2 converges O diverges

A:

Q: Test the series for convergence or divergence. (If the quantity diverges, enter DIVERGES.) (-1)"-1…

A:

Q: dy Differentiate implicitly to find dx e**y = 8x + 3y +8 Evaluate the derivative of the each side of…

A:

Q: x-1 y = log x+1

A: Topic:- derivatives

Q: x3 + x – 1 ;dx J x(x – 1)(x + 5)²"

A:

Q: Differentiate y = -e24x + In(3x – 5). A. 72e24x – 120e24x + 3 y' %D Зх — 5 В. -72e24x + 120e24x + 3…

A: Given query is to find the derivative.

Q: a) Explain why the function f(x) = e#² is not injective (one-to-one) on its natural domain.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 5. Prove lim,40 V2r +I= 1.

A: Given :limx→02x+1=1

Q: For f(x)=3xv(4-x²) determir within its domain..

A:

Q: 2x3 = (3xy + 1)2 Implicit Derivative with Solution and Answer

A: Given : 2x3=(3xy+1)2   To Find : Implicit derivative

Q: In(n+24)158 In(103+12 n)200 The sequence is and its limit is

A:

Q: Using decomposition into partial fractions, 4x2 + 2 -dx x(x² + 2) is equal to In|x (x? + 2)| + C…

A:

Q: Let f(x) = log2(x) and g(x) = cosx. Give the composite fog and go f, and determine their domains.

A: The given functions are: f(x)=log2(x) & g(x)=cos x

Q: y = sinx dy V1+x? sin dy V1+x sinx+x x+x (sin" x)' Jī- dx (sin" x) Vi+x² dx Op tion 2 Option 1 V1-x…

A:

Q: x-1 y = log. x+1

A: Topic:- application of derivatives

Q: x*dy tly' txy) (y+xy)dx =0 3-

A:

Q: Solve the equation xy^3 dx + (y + 1)e^(-x) dy = 0.

A:

Q: 4 Which of the following is the correct expansion of (3x - 3y)2? 9 x2 - 18 xy + 9 y2 9 x2 - 9 y2 9…

A:

Q: Given y, (x) = x? is solution for the differential equation x²y"-3xy' +4y= 0 Using the reduction of…

A:

Q: The solution y, of the homogeneous differential equation y() + 36y" = 0 is O None of them O c_1+c_2…

A:

Q: Find the derivative of f(x)= x% (x% + x% +x%

A: Find the derivative

Q: 25 Type the correct answer in each box. 37 The vector \ / Is reflected across the line Y = 1 and…

A:

Q: Find the differential equation of a family of parabolas with an axis parallel to the x-axis. O y"y –…

A: Option A

Q: 6. Figure out the following limits without applying L'Hopital Rule. sin(r- 4) V2r -1-1 b. lim (2²…

A:

Q: 5. For which values of a and b the following function is continuous at x=-2 3x + a x -2

A: A function f(x) is said to be continuous at a point x=a iff limx→a-f(x)=limx→af(x)=limx→a+f(x)…

Q: cos(xy) + secy = 5

A:

Q: Without evaluating the constants, the partial fraction decomposition for 5x² – 3 f(x) (х3 — 4x)(x2 —…

A: Finding the partial fraction decomposition without evaluating the value of constants

Q: Find the first five terms of the Taylor series for the function f(x) = lnx) about the point a = 2.…

A:

Q: Q3/ Find the limits 1. lim 2. lim Vx+2-1 X-1 х+1

A:

Q: Decide whether the given relation defines a function, and give the domain and range. Year (x) 2005…

A:

Q: y= Arccos(e2x)

A:

Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

A:

Q: Find the angle of the largest right circular cone which can be inscribed in a sphere of radius 9…

A: Given problem:- Find the angle of the largest right circular cone which can be inscribed in a sphere…

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

A: Given :5x2-3(x3-4x)(x2+3x+2)(x2+1)

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

A:

Q: the differential equation (x+y)dy+xdx=o i separable equation C exact equation C

A: We are asked to find whether is exact or separable or  homogenous equation.

Q: Part 4: Solve the following problem. Show your complete solution. 1.) Find the equation of the…

A: A detailed solution is given below.

Q: Indicate a general rule for the nth term of the sequence when a, = 2 and r = a, = (/2)(5y* a, =…

A: Given query is to find the nth term of the sequence.

Q: Green theorem satisfied if the region C is closed True O false O

A: Greens theorem

Q: O (z² - 2x) y" + ( + 2) (2 2) y = 0 O (3x? - 4x) y" - (z + 4) H (e |4) y = 0 (22 + 4) y (4r - 4) y =…

A:

Q: The graph of f is shown. y y = f(x) 6 12 18 24 Evaluate each integral by interpreting it in terms of…

A:

Q: Find and b such that the following function is continuous at x=( [x] – 2a x 0 -

A: To find the values of a and b

Q: Using appropriate trigonometric substitution, dx XV9 — х2 is transformed to

A:

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: