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Q: Define the term standard linear approximation?

A: we have to define the term standard linear approximation.

Q: dt

A:

Q: Latel I, Vx2 + y² dV,

A: answer is in next step

Q: Stsinat dt

A: Given that:∫t.sin2t.dt

Q: In2t To calculate || dt we can use (which method):

A: According to our company policy, we are supposed to answer only one question at a time. For the rest…

Q: vt e dt

A:

Q: Calculate the derivative 5¢6 23 dt dz using Part 2 of the Fundamental Theorem of Calculus. 5,6 23 dt…

A: step 1: recalling fundamental theorem of calculus Step 2: interpreting with the given question step…

Q: What’s the difference between differential and inferential Calculus? And How do they apply to…

A: DIFFERENCE BETWEEN INFERENTIAL AND DIFFERENTIAL CALCULUS:…

Q: Prove the relationship =<- dt

A: we have to calculate  ddt&lt;px&gt;  .....(1) &lt;px&gt;=-ih∫ψ*∂ψ∂xdx .....(2) substituting equation…

Q: the e to ential.

A:

Q: find dy/dx

A:

Q: Define Testing for cointegration when θ is unknown ?

A:

Q: linear a approx Imation differential's to estimate Ja6.96

A: let ,

Q: In(t)dt

A:

Q: Compute all second derivatives of f(1.y) = (x+) e- %3D

A:

Q: 8) Find the linearization of f(x) = 6 + X+1 tan 4 dt at x = 0. 1.

A: On solving this we will get

Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)3

A: First I have find the linearization of x^3 near x=2 and then find the required approximated value.…

Q: How is integration by substitution related to the Chain Rule?

A: The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us…

Q: Let xy = 3 and dy/dt = 4. Find dx/dt when x=2?

A: Given :                xy = 3  , dydt = 4 To find :                      dxdt when x=2

Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)5

A: Given term is (1.999)5Let x = 1.999

Q: 28 dt dz -1

A:

Q: 7. Integrate em***)dx_using the Substitution method. x +3

A: To evaluate the given integral using substitution method.

Q: If X; derive the moment-generating function (mgf) of X?. Ν (μ, σ) :

A: Given X~ N(mu, sigma^2) We want to find the mgf of X^2

Q: d - In(u²) dt dx et

A:

Q: 4х, th dt Vhat is the

A:

Q: Explain Fubini’s Theorem.

A: Fubini's Theorem: If f(x, y) is a continuous function on a rectangle R=[a, b]x[c, d] then the double…

Q: Let xy = 1 and dy/dt = 3. Find dx/dt when x = 1?

A: Consider a function u(x) such that, Now, according to chain rule,  The given information is,

Q: Birinci dereee difrensiyel denk lemin yl1)- Otel Corimino bul. et (t+1) de+ (yey -tet)dy-0

A:

Q: The average rate of change of fx) = ax' Over the interval osxs1 IS a

A:

Q: 5) If y = x³ + 2.x and dx/dt = 5, find dy/dt when x = 2.

A: Q.5) If y=x3+2x and dxdt=5 Find: dydt when x=2

Q: What values of a and b maximize the value of (x – x²) dx? |(Hint: Where is the integrand positive?)

A:

Q: Can i get help step by step please

A:

Q: %3D

A: We are given: u=ln 1-t21+t2⇒dudt=ddtln 1-t21+t2 The derivative can be found as follows:

Q: .3 1+ at dt

A:

Q: If 3xy+x^2=7 and dy/dt=-16, find dx/dt when x=1

A: Derivative, in mathematics the rate of change of a function with respect to a variable. Derivatives…

Q: Use differentials to approximate the value of s2.1. O 100+6ln5 4 O 50+5ln5 2. O 100+5ln5 4. O…

A:

Q: dy+チ=-

A: Note: Since you  have mentioned multiple question, I answered first problem. If you need answer of…

Q: se Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function g(x) : I VR+…

A:

Q: what is the difference is dt and dx in derivatives??

A: ‘dx’ is defined as differential which means a small change with respect to the variable x.‘dt’ is…

Q: Compute the derivative of g(x) .3 = [ 1 dt- 1+ t5 3x2 1+ x15 1+ 25x 3x2 2" In 2 1+ x15 1+ 25a 23 1+…

A:

Q: J7 -dz 21-8

A:

Q: Define Orthogonal Trajectories ?

A: Definition of Orthogonal trajectories:        Given a family of curves , an orthogonal…

Q: Calculate the derivative 26 dt d (6£4 dx using Part 2 of the Fundamental Theorem of Calculus. 26 dt…

A: According to the fundamental theorem o calculus:

Q: If x3 + y3 = 9 and dx/dt = -3, then what is dy/dt when x = 1 and y = 2?

A: Given,

Q: (In x) dx Integrate: 1

A:

Q: Calculate the derivative 25 dt dx using Part 2 of the Fundamental Theorem of Calculus. d dx 25 dt =

A:

Q: Calculate the derivative 33 4:6 dx using Part 2 of the Fundamental Theorem of Calculus. 33 dt = da

A:

Q: dt 4e -et

A: To evaluate the integral: ∫dt4e-t-et Solution: Given integral can be written as:…

Q: Vt3 e-st dt 4s2

A: Explanation of the answer is as follows