1. Find derivative, critical numbers and the absolute maximum and absolute minimum values of f(z) = 1- 4 In(2r - 6) (4,8]. on

Q: PROPER

A: We will solve this homogeneous differential equation.

Q: Learning Task 1: Directions: Solve for y in terms of x (isolate y on one side of the equation and…

A:

Q: Which of the following is equivalent to cos 0? cos 0(1+ tan? 0) sin 0 + tan 0 1+ sec 0 O Option 1 O…

A: Checking all options by simplifying.

Q: Evaluate by separation of variables. dB du = u(1 – u²) sec 3 O 2u? + sin 28 = C – (1 – u²)² O 2 sec…

A:

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (1, 0,…

A: This question is based on finding equation of tangent plane of function having two variables at a…

Q: Q4: Evaluate each of the following integrals: (a) | (4+ cos x)· sin x dx (Substitution)

A:

Q: The value of p for the series En=1n! e¯n by using ratio test is 2 O 8.

A: Ratio Test: Let ∑n=1∞un be a given series such that limn→∞un+1un=ρ Then the series converges iff…

Q: Solve the following items and show your solutions. b.) Identify if the following functions are…

A: 4.

Q: If f (x) 2e²x Then compute f" (0) + 2f' (0) + 2ƒ (0)

A:

Q: *** . ***** ******* . Determine whether the lines intersect, and if so, find the point of…

A: To find the point of intersection of given lines.

Q: Direction: Find the differential equation of the family of curves described. 3. Find the family of…

A: We are asked to find the family of curves of straight lines with slope and `y` -intercept equal.

Q: 2. -7-8X-x²

A: Use substitution method to solve this integration.

Q: Consider the expression (3x² + 2/x)10 a) Find a simplified formula for the general term. (separate…

A:

Q: af Given f(x, y) = In(7x² + 9y²) then

A:

Q: e* +e* –x? - 2 Lim sin? x– x? 2

A: To solve the given limit of the function

Q: Find the general solution of the equation and the specific solutions within the given interval…

A:

Q: Evaluate the integral: J1 +2)³ 11 dx 44 1 22 1 89 O None of these 1 40

A:

Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

A: Given: Here, M=2x-2y2, N=12y2-4xy. Notice that ∂N∂x=-4y=∂M∂y. So, the function is exact.

Q: Find the slope of the line that is tangent to the graph of f(x)=3x²-2 at P(-3, 25). O -3/25 O 27 O…

A: As per the company's guidelines, we are supposed to solve the first question for you, kindly repost…

Q: Find the equation of a cosine curve that is obtained by shifting the graph of y = cos(x) - to the…

A:

Q: Determine whether P = and Q = are orthogonal vectors. If W = and V =, compute V x W. If W = and V =,…

A: Explanation of the answer is as follows

Q: 2. Find the differential equation of the family of circles having their center on the y-axis.

A:

Q: The Maclaurin series for f(x) = x²e=* is E-o(-1)" xn+2 п! False True

A: I am attaching image so that you understand each and every step.

Q: Question Use the First Derivative Test to find the location of all local extrema for the function…

A:

Q: f(x, y) = e2Y sin(x), P(0, 0), Q(2, 1)

A: Use the formula for the directional derivative and simplify.

Q: Find a possible formula for the graph. -8 -7 -6 -5 4 -3-2-1 5678 O g(x) = kx(x + 1)(x– 2) for any…

A:

Q: 3. y = ln³(x + sin x) 4. y = tan¬1(3x) cos 1 4x G ED DI 5. y =

A: All the questions are a solved below.

Q: Solve the following items and show your solutions. a.) Find the general and particular solution of…

A: x dydx+2 y =4x2dydx+2x y =4xComparing with Bernouli's equation;y'+P(x) y = Q(x)P(x)=2x, Q(x)=4x

Q: 3 2 3 3-

A:

Q: 2. Find an equation of the sphere satisfying the given conditions. a. It is concentric with the…

A: In this question, we want to find an equation of a sphere which is concentric with the given sphere.

Q: Evaluate the integral below by interpreting y=f(x) it in terms of areas in the figure. A1 The areas…

A:

Q: A cone was formed by rolling a thin sheet of metalin the form of a sector of a circle 72 cm in…

A:

Q: dy Find for the following expressions: dx а) y = x³ In(3x) b) y = 2 cos (+ 2x3) X 3x2 + 7x + cos (x)…

A:

Q: 21.3 xdx V16 - 9х4 0.

A: We to integrate the given integration.

Q: ................................................. Determine whether the lines intersect, and if so,…

A:

Q: Determine whether the integral is convergent or divergent. 22 Ap 4y – 1 convergent divergent If it…

A:

Q: olve the differential equation with the appropriate method. Finalize answer free of fractions and…

A:

Q: A reservoir is shaped like a square prism. If the area of the base is 225 sq. em., how many liters…

A: Given: Area of the base = 225 cm2

Q: Find the area bounded by the parabola x² = - (y - 1) and the first quadrant.

A: Intersection points:y=0x2=1;x=1 (First quadrant)(1, 0)x=0:1-y=0y=1(0, 1)

Q: Direction: Eliminate the following arbitrary constants to obtain the DE. 5. x = c1coswt + c2 sinwt

A:

Q: dy – (x - y + 1)?dx = 0

A:

Q: S sin-1 x dx A C V1- x2 + C + /1- x2 + C sin x sin x 1 V1 – x² + C D V1- x² + sin x sin x B D E None…

A: To evaluate the given integral.

Q: 2t2 + 38 sinh 16t

A:

Q: Is it log or ln that should be used?

A: You are right. There was a mistake from our end.  Here is the correct explanation: y=x3x Take ln on…

Q: Sv amate the indefinite integral Ancwer in simplest furm (Hactored porm) 1682-9

A:

Q: Question Select your answer. A function f(x) has a critical number a = c. Which of the following…

A: Recall:  y = f(x) + C C > 0 moves f(x) up C < 0 moves f(x) down   Given P(x)=f(x)±k  Where k…

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A:

Q: Solve the elementary applications of Differential equation: 1. The population of a certain country…

A: Given problem:- The population of a certain country is known to increase at a rate proportional to…

Q: What are the values of 8 between 0 and 2n (inclusive of 0 and 2t) that satisfy the trigonometric…

A: tan2θ-3secθ=-3⇒tan2θ-3secθ+3=0⇒2+sec2θ-3secθ=0⇒secθ=2, secθ=1⇒θ=π3+2πn, θ=5π3+2πn, θ=2πn

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

A: