Find the largest interval of existence and uniqueness of solution for the IVP 1 x'+ (sec t)x t-1 * No need to solve the ODE. = TU when x( ) = 1 4

Q: Given h(x)=−2x^2+x+1, find the absolute maximum value over the interval [−3,3].

A: Find h'(x) to find the critical points.The x-coordinate for critical point is (1/4).

Q: If f(x) = (x + 1)²(x+2), find f'(0)

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Q: If y = x + 1* find f''(0)

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Q: If f(x) = 6(a-3/+7), find f'(2). Find f'(5).

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Q: 9. f(x)=T √√5x²

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Q: 3) Determine A and B that makes the function continuous as x approaches 0 and 1? y A x>1 x-B x<0

A: Given:           y=x2                  0≤x≤1A                   x&gt;1x-B             x&lt;0 Given…

Q: Question 2 $-3ar* +2pr² h(r) 4r

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Q: Consider the following function: Step 1 of 4: Determine ƒ'(x) and ƒ"(x). f(x) = (x − 1)(x+8)² Answer…

A: Step 1:To determine f′(x) and f′′(x) for the given function f(x)=(x−1)(x+8)2, we can use the product…

Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: 3 Let f(x) = (x³ + 4x + 7)³. Compute each of the following. f'(x) = ƒ'( − 2) =

A: given  f(x)=(x3+4x+7)3  we know  d(xn)dx=nxn-1d dx(constant)=0

Q: If ƒ(x) = (6x² − 2) (4x + 6), find: f'(x) = Suggestion: Verify using product rule and by simplifying…

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Q: Find the derivative of y = 5x²sec 1(2x-3). O y'= 10x sec-¹(2x-3) + O y'= 10x sec-¹(2x-3) + O y'=…

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Q: (3x) dx 2 x2

A: Note: Since you have posted two questions. As per your comment we are solving the question first.…

Q: m'+4m (1-m*)7

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Q: ylnx Iny da + dy = 0

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Q: For what value of the constant c is the function f continuous on (-∞, +∞)? cz +4 if x ≤ 10 f(x) =…

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Q: 10) The function A how to find how long it will take for the bacteria to reach a total of 5000.…

A: The function 503t represents the amount of bacteria A present in a petri dish after t hours.

Q: F(x)=-4cosx-9tanx , f’(4pi/3)= ___

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Q: Let f(x) f'(1) = = 4x²-3x+6 4x²+2x+8 Evaluate f'(x) at x = 1.

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Q: Find two positive numbers so that the sum of the first and twice the second is 100 and the product…

A: Let two positive numbers are x and y. Given that the sum of the first and twice the second is 100 .…

Q: Find ao of the function f(x) =(T - x)2 |3D | O 5 T^2/12 5 π^2/6 O T^2/12 TT^2/6

A: Fourier coefficient of the function

Q: Car A is 80km east of Car B and begins moving west at 40km/h. At the same moment, Car B begins to…

A: Designate the positions of Car A and Car B at time 𝑡t as xA​(t) and yB​(t), respectively.Given:Car…

Q: r*y" + 31?y" =1+r

A: Consider the provided D.E,

Q: Find ao of the function f(x) = ÷(n - x)² |3D IT ^ 2/12 O 5 T^ 2/6 π^ 2/6 O T^ 2/6 5 π^ 2/12

A: Fourier coefficient ao of the function in the Fourier series

Q: Consider the function f(x)=1/(e^x) -2 List all the x values for which the function is discontinuous

A: Consider the function f(x)=1/(e^x) -2