If f(x) = sin² x, find f'(x) f'(x) = Find f'(2) f'(2) =

Q: nd the equation of the line / in the figure below. Give exact values using the form y = mx + 7= y…

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Q: A curling iron is plugged into an outlet at time t = 0. Its temperature T in degrees Fahrenheit,…

A: I have appended the formula used in the solution part of the question

Q: Use the power series 1 1 + x (-1)^x, x < 1 n = 0 to find a power series for the function, centered…

A: Here we have to find the power series of the given function f(x) = ln(x8+1) and also determine the…

Q: Let P(t) be the population of bacteria in a glass dish, in millions after t hours. suppose we have…

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Q: of an object is given by The displacement = √ ¹ - 7t² + tdt t4 Eveluates for a = 3.85 and b = 9 Give…

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Q: 3. Find the sum of the series k=0 (−1)k2k 62k+¹(2k)!

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Q: Find the inverse function for f(t) = 41e0.25t f-1 (t) =

A: NOTE: Refresh your page if you can't see any equations. . to find an inverse function, interchange…

Q: swer: Evaluate sin(10x) cos(10x) dx.

A: ∫xndx=xn+1n+1+c∫cosxdx=sinx+c

Q: 6 Calculate the area of the surface: b) 13 98√7 20 10 + 15 15 3 64 15 32 15 77 15 16 15 196 7 15 98…

A: The solution is given below

Q: • ey dx = x² dy = 0 - dy dx (1 + x)dy - ydx = 0 = y² − 4, y(0) = −2

A: To find solution of given differential equations.

Q: X SI+√x² 1 + √x 2 x³x² + 2z-2(x + 1) + C - - a. dx 1 1 1 x2 + x2 x + 1 + C 2x² C. 3 x2 + x2 + 2x - 2…

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Q: The accompanying figure shows the graph of a function g(t) with domain 3-4, 04 and range 3-3, 04.…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Let f(x) = x = 202 = f(4). 6x³-11x²-6, x≥ 1.5. Find the value of The value of df1 dx (Type a…

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Q: Suppose the demand for a product is given by D(p) = = A) Calculate the elasticity of demand at a…

A: Given demand function D(p) = -3p + 232 as we know that elasticity of demand ( e ) = dD(p)dp×pD(p)

Q: Let -3 Show all your work. A = Find the unique solution to the system X'= AX satisfying the initial…

A: Please see the below pictures for detailed solution.

Q: 2. Solving differentiable equation a) Find fex) that satisfies the t specified conditions. X8 -…

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Q: For y=2x6−9x3+5x​, find d5y/dx5.

A: Given function:- y=2x6-9x3+5x

Q: Find the derivative u sing the quotient rule. 2x² (3x-3) Y = dy 6x-12 dx (3x-3)² dy dx = dy 6x² 12x²…

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Q: Let y = (5x³ + 9)7 dy dr. Find dy d.x

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Q: Find the particular solution. (x + 1)dy - 2(x + y + 1)dx = 0; when x = 1, y = 4

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Q: dy implicitly x² - y = y³ + x dt dy da O dy da Ody da dy dx = = 2x-1 3y+1 2x+1 3y²-1 11 x-1 3y² +2…

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Q: with initial values y(0) = 1 and y' (0) = -10. A. Write the characteristic equation for the…

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Q: Let f(u)=u4 and g(x)=u=3x3+1. Find (f◦g)′(−1).

A: We have to find out

Q: e the sign change at the transition point F in the figure. y y = f(x) A B CDEF G -X What is the…

A: Given query is to find the correct option for point F.

Q: Evaluate the limit, using L'Hopital's Rule. 1 (1 + x4) ² = lim x Number

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Q: a. f(x) = √√x, over the interval 0<x< 2π and has period 2 b. Sketch a graph of f(x) in the interval…

A: To sketch the given function.

Q: Evaluate the integral. o x sin x sin(x) cos(x) dx

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Q: Find the value of tan (a - B) if cos a = 90° a 180°, and 90° <B<180° 3 5 = -³/³, sin ß = 13

A: Given  cos α = -35,  sin β = 513,  90°&lt;α&lt;180°, and  90°&lt;β&lt;180°.

Q: Find the area of the largest rectangle that can be inscribed in a right triangle with legs of…

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Q: 40. *3 dx o 5x + 1

A: We will use substitution method to solve the definite integral

Q: At which points on the curve y = 1 + 40x³ - 3x³ does the tangent line have the largest slope?

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Q: Use Newton's method to find all real roots of the equation correct to six decimal places. (Enter…

A: Given 2x=1+x3. This can be written as fx=x3-2x+1. Now,  f'x=3x2+2x2 Now, consider: When x=-1, then ,…

Q: Find the derivative of the function. √5-2 √5 +6 f(s) =

A: Given query is to find the derivative of the function.

Q: Compute lim xx x→0+ XX = Number

A: we know that   elnx=xlnxx=xlnxthere for xx=elnxx

Q: If g(x) = sin(x) then g'(x) = g'(3 =

A: Use the definition of the derivative of a function.

Q: We have the following. f(x, y, z) = 7(x² + y²) 2-2-x²-y² 7²-1 a) Express the triple integral "I'…

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Q: A certain population is modeled by the differential equation dy = dx 1.075 (y-2) (y – 5) dy (a) For…

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Q: Apply L'Hôpital's Rule to evaluate the following limit. It may be necessary to apply it more than…

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Q: Kosumi puts the base of a 9-foot ladder 6 feet from the wall of his house. How far up the wall does…

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Q: If f(x,y,z) = 2x² − yz + xz², where x = 2 sint, y = t² − t + 1, and z = e−³t, find f't)

A: from chain rule of derivaties…

Q: ÿ M J +.1.0. = 40.CO.sx...

A: We need to solve Differential equation.

Q: Evaluate the definite integrals for a) b) S/A C) π/6 -9 cos x dx = 8 sec² 0 do = 10 csc t cott dt =

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Q: For the function f(x) = sin(x), write Newton's formula as [A Xn+1 = F(xn) = xn for solving f(x) = 0.…

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Q: Evaluate the definite integral. -3 [₁₁2+. -3 (x+3) ex²+6x+8 dx =

A: ∫exdx=ex+c∫xndx=xn+1n+1+c

Q: 1 f 11 - 1² di 2 dt -1

A: Evaluate the integral

Q: Given the following vectors A=-2a-8a +5a y B=3a +4a-a y X C=5a +4a +6a_ y Evaluate BX(AXC)

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Q: s²+s+1 Exercise 6.4.6: Compute L-1 (2²+ +¹}. $2

A: NOTE: Refresh your page if you can't see any equations. .

Q: Let Z = set of all integers P = set of all prime numbers {1,2,3,4,5,6,7,8,9,10} A = What is ZnPnA?…

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Q: 4. Consider the parametric curve given by x(t) = -7t and y(t) = −3t². (a) Sketch this curve on the…

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Q: Determine which limit is of an indeterminate form. sin x lim X→∞0 X X-3 lim x+3x²-9 lim x→0 X lim…

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