I grad(f)•dr where C is graph of y = x² + 3x from (0,0) to (2, 14) and f (x,y) = ev/lx*•1}

Q: The Trapezoidal Rule with n=6 (namely T6) for approximating / f(x)dx is SPACE FOR YOUR WORK T6 =…

A: It is given that

Q: = f(x) g(x) If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = y 6…

A: The given graph of the functions is shown as,Let,Note:  As mentioned in the instruction, we are…

Q: = = √²* (t²³ + 5t² + 4) dt 0 If f(x)= then f''(x) =

A:

Q: Let f(æ) = In a*(x + 5)*(2² + 4)*| f'(x) =

A: We will use properties of logarithm. lnan = n lna  ln(a.b) = lna + lnb

Q: 2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly…

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Q: with y(0) -1

A:

Q: Find the absolute maximum/minimum if any of f (x)=x' +3x² +1 on the interval [-3, 2].

A:

Q: FIND M'(3) = Page 2 of 4 -1 6 2 g(x) • F(x) LET M (x) = F (g(x)) AND V(x) = 9 (f(x)) 6 FIND V'(3) =

A: Step 1: Step 2: Step 3: Step 4:

Q: Use the graph of f and g. Let p(x) = f(x)g(x) and g(x) 2 (a) Find p'(4). p'(4) = = (b) Find q'(1).…

A:

Q: 4) Let f(x) = - ax"+1 and a x) = 4X-3 5:) f(x) = Fxan? find the 3 first f,g and h. uch that (fo gohl…

A:

Q: f (x) = arctan(e") ad f'(-1) =? find %3D 28 - O A) 1/(e+e3) O B) (e2)/(1+e2) (e2)/(1+e) O D) e/(1+e)…

A: Explanation of the solution is given below....

Q: Find the function F(x) such that F' (x) = 8x and F(0) = 1 O 1+4x^2 O 4x^2

A: topic- Functions

Q: Find S'(-1) if #(f(x))'+ 9z°f(x) = 2 and f(-1) = 2 I'(-1) =

A: To find f'(-1) first we differentiate both sides of  the given equation with respect to x and then…

Q: y=f(x)=x' - 4x +10 find the interval that f(x) graph is concave down. O A) (2, infinite) O B) (0, 3)…

A: Given that the function y=f(x)=x4-4x3+10 Find the interval such that graph of the given function is…

Q: 1) FIND F'): C P)= (x D(2x+)

A:

Q: Find y': y=V5+2 — 2 O y = 7-2x 2√5+2x-x² Oy = √2-2x 1 Oy = 2√5+2x-x² 1-x O y = √5+2x-x2

A: We have to find derivative of given function.

Q: Let f(1) = (1 + 2x + 2)*

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Q: x(t) = Find real-valued closed formulas for the trajectory x(t + 1) = Ax(t), where -4 ^-[33] -4…

A: This is an homogeneous linear differential system. We will solve by this using eigenvalues and…

Q: Σ(+r=1)a-my y=0 = (1 - (1 − π)^^) — -

A:

Q: Find y as a function of x if y(0) = 13, y' (0) = 22, y" (0) = 27. y(x) = y" - 15y" +56y' = 42e*,

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Q: Q2 Q2/If y = (x³ + 5x² + 1)3 + Jsin+/cos³Vtan3x2 find y'

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Q: find dy/dx if y=((t-1)/(t+1))^2 and x= (1/t^2)-1 at t=2

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Q: f'(x) = = Lº 1 + sec(7t) dr f(x) = sec (2) + 6 X Vì Hint: +== f*√²- 1 + sec (7t) dt = - √1+ sec(71)…

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Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

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Q: Find y as a function of x if y" + 16y' = 0, y(0) = 0, y'(0) = 4, y'(0) = -32. y(x) =

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Q: 5 Find *: (a) y = cos(11x + 2x) dy

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Q: d[cos(x*)] dx (2k+1)! (-1)*2,* - (2k)! .(-1)시2x4~2 (2k+1)! (-1)*2x*-3 E (2k+1)! None (-1)*-'2x*-1 E…

A:

Q: Let f(x) = 6x* /T + f'(x) =

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.