f(t) dt = x2 + x – 2.

Q: x2y3-y=x+x2 find dy/dt

A:

Q: V49 – t dt t3 Integrate: -C

A: I=∫49-t4t3dt

Q: 3x u2 – 1 _a) h(x) = sin* t dt (b)g(s) = (t – t²)dt (c)g(x) = || -du u² + 1 2x

A:

Q: Determine whether the equilibrium at x = 0 is stable, unstable, or semi-stable. xp -x7 dt The…

A: Determine whether the equilibrium at x=0 is stable,unstable orsemi-stable.dxdt=4x2-x7

Q: use Separation of Variables to find the general solution. dx/dt= (t + 1)(x2 + 1)

A:

Q: 3. If 2 = x² – x* + 6x – 5, then dty evaluated at x = 1 is dx4 dx (А) 8 (B) 36 (C) 96 (D) 120

A: To calculate the nth derivative of function y, differentiate y four times with respect to…

Q: d²x_dx Verify that x = C,e¬t + C2e2t is a solution to dt2 2х — 0. - dt

A: To verify the given statement.

Q: If g(x) = - [e' - In(2t+1)]dt, find g''(x) . dx A e* -In(2x+1) 4 B (2x + 1)² 4 C (2x + 1)² 2 D (2x +…

A: To solve the following problem

Q: f(x, y) = xVy + y²; (2, 1)

A: The function is fx,y=xy+y2.   Determine the partial derivative with respect to x.…

Q: Find the first order partial derivatives of the function, w=xz-5(x^2)(y^3)(z^4)+ln(x*y^2*z).

A: w(x,y,z)=xz-5x2y3z4+ln(xy2z)

Q: Find the minimum and maximum of A over a particular interval [0,6]. A(x) = f(t) dt

A: The solution is given below in the next step: I

Q: Find the linearization of f(x) = 9 – dt at x = 1. 2+t

A:

Q: 3 62 what is 13 | f(t) dt? f(x)dx = 3 6.

A:

Q: secx 1 Given g(x) : z dt , find g'(x). t2

A: gx = ∫7sexcx1t2dt           = ∫7sexcx t-2 dt        = t-2+1-2+7secx      =t-17secx-1 = secx-1-7-1-1…

Q: d Use the chain rule to calculate f(x), if f(x) dx, dt. -x12 f(x) =

A:

Q: Find the first partial derivatives of the function. f(x, t) = t©e¬x fx(x, t) = f:(x, t)

A: To find the first partial derivatives of the function: f(x,t)=t6e-x

Q: f(2) = | : t2 – 1 dt 1+ cos² (t) At what value of ¤| does the local max of f(x) occur?

A: Given that a function f(x) and we find value of x does the local maxima of f(x) occurred. We know…

Q: 5. dt3 d³x(t) 8 d²x(t) dx(t) - - dt + x(t) = u(t) 14 dt2 d²x(0) 1, dx(0) x(0) = 1 -2, dt2 dt

A: Given below the detailed solution

Q: . Find all the second-order partial derivatives of the function z = f(x, y) = e2xe"

A:

Q: Find all the second partial derivatives of the function a) f(x,y) = x* – 3x²y³. %3D | b) f(x,y) =…

A:

Q: Solve the initial value problem for y as a function of x. (x² + 25) dy %3D 29, у(5) %3D 0 dx

A:

Q: Compute the given partial derivative. f(x, y) = e2xy – 3x²y°, (2,1)

A:

Q: Find the partial derivatives of the function f(x, y) = | cos(4t – 5t – 7) dt

A: Given function is

Q: Find the second order partial derivatives of the function: f(x,y)=x* +xy° +x+4.

A: In the case of function of two variables there will be a total of four possible second order…

Q: Find all second partial derivatives of the function f(x, y) = xy + x° + y at the point xo = (2,4). =…

A: Consider the case of a function of two variables, f(x,y) since both of the first order partial…

Q: 02/ Solve the system derivative to find the general solution of each (x & y as a funtion of t). dr…

A:

Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t     x(t) general function solutions

A: This system has been solved by the elimination method, by eliminating y to get the general solution…

Q: Find the partial derivative fx for the function f(x,y)=√16x+y³ |f₂(x, y) = O f.(x,y)= f₂(x, y) = 1…

A: We have to find derivative

Q: b. g(x) = [ cos(r*)dt x²+5x F(x)= [,(6r* +6e° )dt с. 6t +6e" dt

A: We have to find derivative

Q: Find a value of x such that

A:

Q: b. Find the partial derivatives fx ,fy of the f (x,y) = x². e²y+3x

A:

Q: Let Dx be the linear transformation from C'[a, b] into Cla, b]. Find the preimage of the function.…

A:

Q: d Use the chain rule to calculate f(x) if f(x) In (1+ tº) dt. dx, 0. f(x) =

A: let's use chain rule and find derivative of integral.

Q: A) Find the linearization of the function at the given point. f (x, y) = 1+ y ln (6 – xy), at (5, 1)…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: find ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: Given function is fx,y,z=x2+y2-2z2+zlnx and point=1,1,1

Q: Suppose that , g(t) dt = v2 g(r) dr V2 b [-g(x)] dx а. -3

A: Given: ∫-30g(t)dt=2. The objective is to find, ∫-30-g(x)dx ∫-30g(r)dr2

Q: Find the differential dy of each function: a) f(x) = 2x^1/3 - 3x^1/2 b) f(x) = ( x^2 +1) / (x+1)

A: we will find the derivative of given function using basic differentiation rules.

Q: Solve the IVP 3 d.x dx a(0) = 1, = 2. dt \t=0 dt2 dt

A: Given d2xdt2=-x(dxdt)3, x(0)=1, dxdt|t=0=2

Q: If X+y = x-y x2. -y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0? О 12 O -12 12

A:

Q: 1 Find F'(0) given that F(x) dt. In(t + 1) 2x

A:

Q: dx = x(x 1)(x + 1) dt has a solution that is

A:

Q: (b) If g(x) = [,! 1 dt, find g'(x) 4+t2

A:

Q: Find the linearization of the function f(x)=x5 at x=1. L(x)= Using this linearlization, f(1.04).is…

A:

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.: y2 - 8x3 = -55; dx/dt…

A: y2-8x3=-55, dx/dt=-4x=2,y=3

Q: d²x dx + 4- + 5x – 10 = 0, when t = 0, x = 0,x = 0 dt2 dt

A:

Q: (b). Examine the behavior of e*+iy as x → -.

A: Euler's formula states that for any real number x  Any complex number z = x + iy,  can be written…

Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…

Q: d If g(x) == _S^*[e' − In(2t+1)]dt, find g ''(x) . - dx -2 2 A (2x + 1)² 4 B (2x + 1)² 4 (2x+1)2…

A:

Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: