Determine the rate of change of the function g(x,y) = y²tan (x-2y +4) at point (12) in the direction of the vector V-27-23.

Q: Solve for the particular solution: 4e-32-2 y = e-6x +3e-3x+2 ; y(0) = 1

A: Given differential equation  y'=4e-3x-2e-6x+3e-3x+2  ; y(0)=1 Rewrite the differential equation as…

Q: f(x)=√√(ax + b), find f(4)(x).

A:

Q: D Question 8 In the Four-Step Rule, why is the cancellation of the Ax terms allowed even if Ax→ 0 is…

A: Solution

Q: Find the equation of the tangent line to the graph of f (x) = 6x2 - 4x + 1, at x=1.

A:

Q: If you know that lim f(x) exists at an interior point of a domain interval of f, can you find its…

A:

Q: Which of the following are anti-derivatives of y' = sin æcosx ? I. F(x) = sin² ² + C II. F(x) =…

A: Topic = Integration I and III only correct

Q: t f(x, y) = x² cos(xy). ) Determine f(x, y). Determine fy(x, y). Determine Vƒ(1, π).

A: Topic:- application of derivatives     Note:- as per our guideline if more than three subparts…

Q: Find the linear approximation of f(x)=√x when x = -27.

A: Linear approximation is an approximation of a general function using a linear function. It is useful…

Q: Find an equation of the line containing the given points. Use function notation to write the…

A: Find an equation of the line containing the given points. Use function notation to write the…

Q: What is the derivative of f(x)= xe ?

A: To find the derivative.

Q: y = 3x³-2 5x243

A:

Q: Find the distance between the skew lines =(4,-2,-1)+1(1,4,-3) and F=(7,-18,2)+u(-3,2,-5).

A: Given lines:- l1:r→=4,-2,-1+t1,4,-3 l2:r→=7,-18,2+u-3,2,-5

Q: Direction : Write the expresion in alebragic form  (9) sin(arc sec x

A:

Q: 1. Calculate the following limits (showing all working): log₂ (n) + 2n no log3 (n) + 3n (a) lim √7n7…

A: We have to find the limits.

Q: Kindly answer 6 and 7

A: Need to find out that the given differential equation is exact or not.

Q: What is the probability that an officer was promoted or a woman?

A:

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A:

Q: 4. G(x) = n x3.4 -5me + p 5. F(x) = ax³ bx² + cx - d 6. f(x) = (3x + 1) (2x7 - x + 2)

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

Q: 57-62. Transcendental functions Determine the end behavior of the following transcendental functions…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: (-7)=|

A: Topic:- derivatives

Q: [We dx = + C

A:

Q: Find(x(ax+b)), where a and b are constants (a) x(ax+b) ax(1 + ln x) (b) x(ax+b) (x + ax ln x + b)…

A: To find:ddxxax+b

Q: Find 원 when ax + cos(by) = c, where a, b and c are constants. b (a) —-cscy (c)csc(by) b (b) -…

A:

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: y=(2+x)2(1-x)3

Q: let a and b be integers such that 7 divides both a+3b and a-2b. Show that 7 divides a

A: Given 7 divides a+3b and a-2b  Then 7 divides (a+3b)+(a-2b)= a+b  And 7 divides (a+3b)-(a-2b)=5b…

Q: Use a local linear approximation to approximate the value of 6(1.99)2 +3.02 by a rational number.

A:

Q: Find the following using the table below. I 1 2 3 4 f(x) 4 2 3 1 f'(x) 1 2 3 4 4 g(x) g'(x) 4 2 AN…

A:

Q: d Let Arctan² (3e) dx ke*Arctan(f(x)) g(x) Compute kf (0) - g (0) - 3

A:

Q: Let g be a differentiable function of two variables, with first variable x and second variable y,…

A:

Q: Find the solution of the IVP Then, evaluate y(1.063). x²y" = (y')², y(1) = 0, y′(1) = −1

A: Given 1. x2y"=y'2 2. y1=0 3. y'1=-1

Q: 21-44. Determining limits analytically Determine the following limits. 26. (x-4) x-2+ x(x + 2) (x-4)…

A: 26. The given limits are, a) limx→-2-x-4xx+2 b) limx→-2+x-4xx+2 c) limx→-2x-4xx+2 Note:    Since…

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.

A: Given, y=x2-1x

Q: c) h(t): 5t e (t² + 1)^

A:

Q: Solutions

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Q: Evaluate the following integral. [x²√7z+3 dz dx

A: The objective of the question is evaluate the indefinite integral.

Q: -+-N=r; N(2)=8. dt t

A: we will find the required.

Q: The D.E. (y+1) dx + (4x−y) dy=0 has an integrating factor because N ƏM dy ƏN dx is found to be

A: Let's find integration factor for given differential equation.

Q: Make an ORIGINAL EXAMPLE OF "Variable Separable" A) GIVEN B) SOLUTION C) ANSWER D) WITH EXPLANATION

A: Given expression, Solve 1+x2dydx=1+y2

Q: 44. Suppose that f(4) = 2, g(4) = 5, f'(4) = 6, and g'(4) = -3. Find h'(4). (a) h(x) = 3f(x) + 8g(x)…

A: Simply use differential formula and we can easily solve it Please see the solution Thanks

Q: Where did the -1/3 come from? Is it because the 3 is the nth root and the 1 is the one inside the…

A:

Q: Question 9 Find the slope of the line that is tangent to the graph of f(x) (E) None of the choices 2…

A:

Q: Given two differentiable functions fand g, the derivative of the function f(x) - g(x) can be…

A: Given:- f and g are two differentiable functions

Q: 1. Find the general solution: y"

A:

Q: 1. Given the algebraic function x² xy + y² = 3

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Q: etermining the Maximum and Minimum Values of Quadratic Functions rocket is launched in the air. Its…

A: Given query is to find the maximum height attained by the rock.

Q: 2 Given tane = find csc0, cos0, sec, cot0, sinė if 0 is in Quadrant III. 3

A: Given  tan θ = 23.

Q: (1) Given f(x)=2x+√x, find (ƒ-¹) (3)

A:

Q: 2014 O ०.२ ०.०२ 0.02 0.08 0.4 0.6 0.16 0.8 1.0 ।.२ 1.4 0.98 or 0.32 0.5 0.72

A:

Q: u 2.) du + (-1/2 − u²)dt = 0 t

A:

Q: .Find the position and velocity vectors of a particle that has the given acceleration and the given…

A: Given :- a(t) = 4i- 72j+ (72t + 4)k v(0) = i+ k r(0) = j+ 3k