Given the function f(x) = -√x + √³, find f'(6). Express your 4' answer as a single fraction in simplest radical form.

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Q: P(2,-3,4), Q(4,4,5), T(1,2,7) forms a triangle. find the vector projection of QP parallel on QT.

A: Proj. of QP→ on QT→ = QP→·QT→QT→WhereQP→ = Q-PQT→ = Q-T --------------------------------------------…

Q: A continuous O Ext F(XI = Find ***** V-V- K x has CDF X Co oxx cl 15X value of k 16 17 18 19 20 21…

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Q: Complete the table. (Round your answers to four decimal places.) X-7 x-7x²²-8x+7 x 6.9 6.99 6.999 7…

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A: Function f(x)=e-0.5x(4-x)-2Derivative of f(x)=f'(x)

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Q: 12. -s-7 (s+1)(S-2)

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Q: 2- Determine lim[ v( x-1000)+10]/x x-0

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Q: пр 4. STIS df x²s 5. Evaluat

A: I=∫0π3  x2 sin3x dxIntegration by parts;u=x2, v=sin 3xI=x2∫sin3x dx-∫(2x ∫sin3x dx)  dxI=-x2…

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A: We can find the domain of the equation as below.

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A: Find your answer below

Q: 31. (a) 32. (a) 33. (a) 12x-1| dx √2 + x) dx e* - 1| dx L'i lex -3π/4 (b) cos x dx (b) [*/² | } −…

A: Given: ∫-11ex-1dx

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A: Since the student has posted multiple questions and does not mention any specific question, so we…

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A: Solved below

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Q: Find the slope of the normal line to the graph of g(x) = = at the point where x = 0. sin¯¹(x)+e²

A: Slope of the Normal line to the curve f(x) is -1f'(x).

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A: (i) Given that the tangent line the graph of the function at the given point  g(x) = (6/7) x+ 1…

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A: Given: r(t)=t i+6ti

Q: Find the average value of ƒ(x) = x² √√28 + x² on the interval [0,2]. favg= Report all answers…

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Q: 11. lim [w ln (1-2)] In 3w

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A: Take the partial derivative of coefficient of dx and dy to show that the given differential equation…

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A: Let's find.

Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

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Q: Solve the given differential equation. All solutions should be found. dy 2xy + y² + 7 dx x² + 2xy…

A: To find the solution of given differential equation in implicit form.

Q: Use the Product Rule to differentiate the function. f(x)= x cos(x) F'(x) =

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Q: Ex: Solve the DE x²y"-5xy' +9y=0

A: To find the solution of the given differential equation.

Q: IV. Do as indicated. 1. Let f(x)= where z = 1. 1 ²+1 Find the equation of the tangent line to the…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = -2x - (sin(x))² Read It Need…

A: We can solve this as follows:

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Q: Find the laplace transform of ƒ (t) = 3t³ − 2e²t + 2 cos 2t OF (S) = OF (s) = OF (s) = OF (s) = OF…

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Q: Determine any planes that are parallel or identical. (Select all that apply.) OP₁: -60x + 90y + 60z…

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Q: The height y (in feet) of a ball thrown by a child is 1 -x² + 2x + 5 y = 16 where is the horizontal…

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A: Given : f(x)= csc(x)

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A: we have to find curvature.

Q: Solve the following differential equations of d²y_2dy + y = 2x dx² dx

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Q: Evaluat the integral:- 푼 is S. sec (cosx) dx dy D Sin y

A: Here, to evaluate: ∫01∫sin-1yπ2sec2(cos x) dx dy So, the region of integration is bounded by the…