Let H(x)=f(x)-g(x). If f(x)5x2 and g(x)=2x3 , what is h'(1)?  a)4 b)16 c)6 d)10

Q: Let c>0 be a constant.  Is this result true or false?

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Q: Find the most general antiderivative of f(x) = -3x – 7xL7. Note: Any arbitrary constants used must…

A: Topic = Integration

Q: What is the maximum value of y = cos x. For - < x < < ?? 1 1/2 2.

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Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

Q: Find the local linear approximation of f(x) at 4 + x xo = 3, where Ax = x – 3. NOTE: Enter the exact…

A: f(x)=14+x

Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: Sx, ifx 1 f(x) = Show that f is R- integrable.

A: R- integrable function

Q: usk 2: Find the derivative of 4x2 + 6y3 = 50 by filling the blanks. %3D (2 xD(x-)+x 6)(y³4)_=__ dy >…

A: We have, 4x2+6y3=50            ⋯⋯1 We know that, from basic derivative formula ddxkxn=n·kxn-1ddxk=0…

Q: If fCx) is bdd Junchion an f(x) dx = の-3 then 3. True or Fal se ?

A: Solution :- An odd function is defined such that f(−x)=−f(x)

Q: dy Prove that dx of x2 +2x is f'(x)=2x + 2

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Q: dy + ydx %3D 3x²y?dx,

A: Given differential equation is bernaulli's differential equation.,  and we can solve it by reducing…

Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction ef 4i - 3i

A: The directional derivative of a function f(x, y) in the direction of the unit vector (a, b) is given…

Q: Verify the statement by showing that the derivative of the right side is equal to the integrand on…

A: We will find the derivative of right side. By showing this derivative equal to integrand the…

Q: \+etari), find f.. S, and f.- xyz 3. If f(x,y,z)= hn 2

A: We have to find fx , fy , fz.

Q: The maximum value of y = cos x for - < x< is 1

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Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

Q: Suppose F(x,y)=sin²(xy +e"), where x=u² +v and y = In(u² +v). Find the . ƏF ¸ ÔF value of when u =1…

A: The given function is: F(x,y)=sin2xy+eywhere:x=u2+v         and         y=lnu2+v

Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: 5) What is the maximum value of y = 5 Cos 4x ?

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Q: A particle is moved along the x-axis by a force F(x) = x² + 5x – 6 . How much work is done in moving…

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Q: The derivative of f(z) - (+10z) is O6z (2z + 10) O6z (2z+10) O 6z (2z + 10) O 6z+60

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Q: Suppose that f(x, y, z) = (1+x + y² + z³)4 + ln (1 + 3x + 2y + z).

A: In this question, we approximate the function by using a linear approximation of f(x,y,z)

Q: 2. Use second order derivative to derive the acceleration, a for an object that falls where its…

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Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

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Q: Y2-1 dy

A: Follow the procedure given below.

Q: What is the derivative of y x2 e+ 3x -2 ? %3D O y = (6x³ + 3x? +2) ez?+2z - 2 %3D O y = (6x + 3)…

A: Topic = Derivataive

Q: In integrating the function fx* in Sx dx using integration by parts, what would you choose for your…

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Q: Compute the derivatives of the given functions. f(2) = In (7z²). 7a?). f'(x): / (z) = help…

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Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

Q: Use 4-segment the trapezoidal rule to numerically integrate f(x) = f(x)=∛(44x-4) from a = 44 to b…

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Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Let f (x, y) = 2x³ + 4y³ + 19xy Find D = frx · fyy - fey at the point (2,2)

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Q: Solve the nonhomogeneous ODE by variation of parameters. ODE: y" + 4y = cosh 2x

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.  g(x)=…

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Q: Verify Young's Theorem f(x,y) = e(2x+y) In(xy)

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Q: 2an-butn Converge bey to

A: The given sequence is an.bnn=1∞ we observe that there is N1&gt;0, so that when n&gt;N1, we have…

Q: what is the maximum value of y=sinx, 0 less than or equal to x less than or equal to 2pie, and…

A: Given function  y = sinx on  0≤x≤2π

Q: Find the fourth derivative of f (z) = 27 + In (z) – 160z. %3D

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Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

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Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: 3. Verify the statement by showing that the derivative of the right side is equal to the integrand…

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Q: Integrate f(x) = 10 ( 1 – x)9 where 1 ≤ x ≤ 3, Using Boole’s rule

A: The function f(x)=101-x9 where 1≤x≤3. We have to integrate this integral using the Boole's Rule.

Q: Find the orthogonal trajectories of the functen X + ce-X which is . passing Thieugh (-2.0)

A: We need to find the orthogonal trajectories of the function y=x+ce-x, which is passing through (-2,…

Q: Confirm the approximations by using the linear approximation at x = 0

A: