(4) Use logarithmic differentiation to find the derivative of the following function. y = x¹/x

Q: or each function h(x), find two functions f(x) and g(x) such that h(x) = f(g(x)) a) h(x)=√x² + 3 b)…

A: Topic:- function

Q: Determine the scalar equation of the plane containing the point (-2, 9, 7) and 9. perpendicular to…

A:

Q: A box with square base and open top has a volume of 1000 m³. Find the dimensions of the box which…

A: This question can be solved using the concept of maxima and minima.

Q: Which of the following is an exact DE? A. (x² + 1)dx - xydy = 0 B. xdy + (3x - 2y)dx = 0 C. 2xydx…

A: Solution:

Q: Find the horizontal and vertical asymptotes of this curve. 2x²+x-1 y= = x²+x-2

A: Given.

Q: Express the repeating decimal as a fraction. 0.789626262626... 0.789626262626... =

A:

Q: Question 3 limx→+∞ e-√√ OI Oll O III OIV O Not Indeterminate

A:

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

A: The given function: gx=-4ex.We need to find the slope of the function at the given point.

Q: (x + 1, x 0 Can also be displayed as: x + 1 when x 0 f(x) = Is f(x) continuous at x = 0? Why or why…

A: We have to find the solution of continuity

Q: * The z-transform of a signal is given below,its final value Z-1 2-¹ (1-2-4) x(z) = 0.25 (1-z-¹)²…

A:

Q: If f'(x) = 2x³ + 3x² − 4x + 5 and f(0) = 1 and f'(0) = 2 find f.

A:

Q: lim,+1+(1²-2-²-1) In

A:

Q: 4) a) Determine the derivative dx of the following functions y = 3** b) 1-3- 3e² 1² c) y d) y =…

A: We have to find the derivative.

Q: 5.1 Let a eR, v = 4ai - 6j and w=a²i +3j. Determine all nonzero values a, if any, so that is…

A:

Q: e costu(t) e-¹ u(t) Option 3 Option 4 • What is inverse Laplace for 1 (s + 1)² + 1 y (s) = te¹ u(t)…

A:

Q: # Determine whether the function z = f(x, y) = (why or why not) for for (x, y) = (0,0) (x, y) =…

A:

Q: Use any method to determine whether the series converge. ∞ 1 (2) Σ 4k k=1 The series (5) Σ k=1 The…

A:

Q: Suppose you have a 1024 mg sample of a substance known to have a half-life of 50 years. Find the…

A: Given half-life of sample=50 yrs and the initial sample is = 1024mg.

Q: Q3/ Solve dy dx4 2d²y + 1 = 0 dx²

A: Given d4ydx4-2d2ydx2+1=0To find solution:

Q: A coffee merchant sells three blends of coffee. A bag of the house blend contains 100 grams of…

A: This question can be solved using the concept of system of linear equation.

Q: TT/6 6² tan 2x dx =

A:

Q: 13. Determine the distance between the following lines. [x, y, z]= [4,5,9]+s[-3,4,-9] and [x, y, z]=…

A: Above question is solved.

Q: lim √25t2 + 2-5t

A:

Q: Determine dx for each of the following functions. Do not simplify the dy expressions after applying…

A:

Q: he polar equation for circle x^2+(y- 3)^2 =9

A:

Q: 1) e5Ln x+4Lny-Ln z 2) 2Ln√x + 2Lnez - 2Lne* Rewrite the following quantities

A: Given :1. e5Lnx+4Lny-Lnz2. 2Lnx+2Lnex-2Lnex

Q: Solve the following Differential Equations with Laplace Transforms y" - by' + 15y = 2 sin (3t), y…

A:

Q: Calculate the value of the following limits algebraically, (if they exist): 2x²-3x-9 a) lim x-3 x-3…

A:

Q: Let ā (3, 5, - 4) and 6 = (1, 4, 3). (à − b ) × ( ã + b) =

A:

Q: 5: Evaluate I where D is the rigion bounded by xy ve x+y = 7 SS (X+Y) DA D (1

A:

Q: 4. Draw a sketch of the following angles. Identify the acute related angle (a) and draw the related…

A: Topic:- trigonometry

Q: Q22) The inverse Laplace transform of H(s) : = a) f(t) ==e¹+¹e²t 8 8 -3 c) f(t) == est +²e-2t 8 8 1…

A: To find the inverse laplace transform of givem function.

Q: 1 Given f(x)=³-57² +24r, which of the critical number found in the previous number is f(c) a…

A: You must have an idea about to how to find relative maximum or minimum using critical points.

Q: cos(etan 3x) y cos

A: The given function y=cosetan3x

Q: * Define this property L (f(t)eat) = F(s-a) Second shifting property O Linearity property O…

A:

Q: Q1) L-1 a) cosht -1 b) 1 - cosht c) (cosh2t - 1) d)/(1-cosh2t) Q2) The general solution of y"" + 2y"…

A:

Q: (2x -۱۱۶ (3x44795

A:

Q: Solve the following initial value problem for r as a function of t d²r Differential equation:…

A:

Q: If [ f(x) dx = 12. g(x) dx = -2 and L₁ dr following gives the value of [[1²)+ 4 76 Sh +4g(x)- h(x)…

A: Given:     ∫-36fxdx=12     ∫-36gxdx=-2     ∫-36hxdx=-7

Q: 6 sinh t 6 cosh 51 Option 2 O Option 3 * What is inverse Laplace for 6s s² +25 6 sint 6 cos 5t…

A: In this question, we need to find the inverse Laplace of given function.

Q: that equals 1 2 3 -5 49 2 7 6.

A:

Q: 4.1 Evaluate the integral [3√x √(3√x - 1 / +5 4 + x² expressions after applying the integration…

A: We have to evaluate the integral

Q: J (secs x) dx/csc x

A:

Q: Question 4 (a) Solve the following: √4x² dx (b) Explain with the aid of a sketch how this value can…

A: Let's solve given integral.

Q: Q1) L-1 s(s²-1) = a) cosht-1 Q2) The general solution of y"" + 2y"-y' - 2y = 0, is: a) y(x) = c₁e²x…

A:

Q: 2.2 2.3 Determine whether the series below converges or diverges. Determine the first four terms in…

A:

Q: Express the repeating decimal as a fraction. 0.474747...

A: Let's express as a fraction.

Q: lim (√x² + 4x +1 − x) x→∞

A:

Q: Let ā 47- 57 and b - 27 + 3j + 4k. Find - 2ā - 36.

A:

Q: | 1) 2Ln(√x + 3) + 2Ln(√x − 1) = Ln(6x - 7) 2)3x+2 = 27

A: This question is related to solution of equations, we will solve it using given information.