Is it possible that some constant-a exists such that a^x = (d/dx)(a^x)? In other words, is there some function y(x)=a^x such that y=y'? In other words, is there some function that is its own derivative? Determine a.
Is it possible that some constant-a exists such that a^x = (d/dx)(a^x)? In other words, is...
vector calculus. Do both please Q1: What, in your own words, is the difference between a partial derivative and a directional derivative? How are they similar? Give a particular example to illustrate your explanations (choose some function z=f(x,y)) Q2: Given a surface z= f(x,y), a point (x,yo) in the domain of f, and a unit vector i pointing some direction in the xy-plane, what does it mean if D,f(x,Y)=0? Be as specific as possible. Q1: What, in your own words,...
Tutorial Exercise Evaluate the integral using the substitution rule. sin(x) 1/3 1* dx cos(x) Step 1 of 4 To integrate using substitution, choose u to be some function in the integrand whose derivative (or some constant multiple of whose derivative) is a factor of the integrand. Rewriting a quotient as a product can help to identify u and its derivative. 70/3 1." sin(x) dx = L" (cos(x) since) dx cos?(X) Notice that do (cos(x)) = and this derivative is a...
calculo 1- Given the function y = (4-x^2 ) + 4 * arcsen (x/2) Get dy/dx and its value for x 0 (this year is requested to find the value of the pending for the function given in Point X :0). 2- Is yarcta n ((x +3)/(1-3x) Find his derivative 3- Determine dy,/ dx and the value at the point (using implied derivation) 2x 2 y 2-3xy 1 0 3x2Уз + 3xy2 +1-6+,5 2xy + sen(y) # 2 6 Determine...
(a) Find the derivative. y = In(4x – 5) – 3 In(x) dy dx (b) Find the derivative. 4x - y = = In dx State whether the function in part (b) is the same function as that in part (a). The function in part (b) is the same function as that in part (a). The function in part (b) is not the same function as that in part (a).
If f(x, y) is continuous in an open rectangle R = (a, b) x (c, d) in the xy-plane that contains the point (xo, Yo), then there exists a solution y(x) to the initial-value problem dy = f(x, y), y(xo) = yo, dx that is defined in an open interval I = (a, b) containing xo. In addition, if the partial derivative Ofjay is continuous in R, then the solution y(x) of the given equation is unique. For the initial-value...
please explain the steps to your solution using Microsoft excel to Compute the answer 7) From x-1 tox-2, find the values of the function whose derivative is dy Inx) + xy dx using the 2"d order Runge-Kutta approximation and a Ax of 0.1. At x 1, y-1. 7) From x-1 tox-2, find the values of the function whose derivative is dy Inx) + xy dx using the 2"d order Runge-Kutta approximation and a Ax of 0.1. At x 1, y-1.
1) Suppose that the function v in the Product Rule has a constant value c. What does the product rule then say? What does this say about the constant multiple rule? 2) Graph y = tanx and its derivative on (-1/2, T/2). Does the graph of the tangent function appear to have a smallest slope? A largest slope? Is the slope ever negative? Give reasons for your answers. 3) Explain why the following statements are true or false. a) If...
need asap se the properties of limits to help decide whether the limit exists. If the limit exists, find its value. 7) lim+12xs+27 x-+-9x+9 A) 216 B) 12 C) Does not existD)-6 ifferentiate. 8)f(x) =4x4-7x3-3 8) , A) f'(x) = 16x3-21x2-7 C) f(x) = 4x3 + 3x2 B) Px)-4x3 3x2-7 D) f(x) 16x3 -21x2 9) y (2 2 9) dy )4.6x5 + 20x3 + 24x B)-=6x5 + 24x3 + 24x c a24x3+24x = 6x5 +12x3 +12x D) dx 10) 10)...
Let ψ(x, t) describe a free particle and < x> = ∫ψ(x, t)* x ψ(x, t) dx, show that (d2/dt2) < > = 0, where x is not an explicit function of t. What is the physical meaning of this second order derivative? Let v(x, t) describe a free particle and<x >- y(x, t)* x ψ(x, t) dx, show that (d3dt) < x >-0, where x is not an explicit function of t. What is the physical meaning of this...
x dx dy + y) dx dy 0 (b (d a)(c) Answer: (a) x dx dy + y) dx dy 0 (b (d a)(c) Answer: (a)