x-2 ifx<3 Let f(x) = 1 if 3sxs4. x+3 if x>4 a. Find lim f(x). b. Find lim f(x). x3 X-4 Select the correct choice and, if necessary, fill in the answer box to complete your choice. O A. lim = x-3 B. The limit is not - oo or oo and does not exist.

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A: Given that: y''+5y'+372y=0y(0)=-2, y'(0)=7y=eat(c1cos(bt)+c2sin(bt))

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Q: a The integral that represents the length of the curve 7 (t) = <2/t,cos (2t3/2), sin (2t3/2)) where ...

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Q: For the following differential equations, determine a. order b. degree c. linearity(yes or no) d...

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Q: find the differential equation of y'' + 5y' + 6y = 0 when y (0) = -1, y' (1) = 3

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Q: 12) 39 12.6 В

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Q: Find the partial sum S, for a geometric series such that a4 = 48, ag 1536, and n = :9. Sum =

A: Given that: a4=48a9=1536n=9

Q: Use the figure to find the exact value of the trigonometric function. Find cos 20. 3.

A: We can find the value of cos2 theta as below from the figure

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A: ∫z7(10z8-4)dzGiven that: 

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Q: Evaluate the integral (7 – 2x) dæ by interpreting it in terms of area. Answer:

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Q: Evaluate the definite integral: | (42 2 – 6) da

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Q: 2 dx (х-3)6 V-x2+6х-5

A: Given:      ∫2x-36-x2+6x-5dx     =2∫1x-36-x2+6x-5dx substitute u=x-3→dudx=1→dx=du                  x...

Q: E. Find the cartesian equation of the following:

A: Given that: 94sin(2θ)=r2

Q: If h(x)= (-2+8x+8x^2) (7x+2x^6+7x^7) then h(x)=f(x)g(x) wher

A: Given that: h(x)=(-2+8x+8x2)(7x+2x6+7x7)

Q: Convert the following number in the indicated base. 6701 to base 15

A: Divide the number repeatedly by 15 until the quotient becomes 0. When 6701 is divided by 15, the qu...

Q: Consider the differential equation x?y" – 8xy' + 20y = 0; x4, x5, (0, ∞). Verify that the given func...

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Q: Find the derivative of the function. g(x) = (1 + 5x)5(4 + x – x²)7 - g'(x)

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Q: -2 -1 1 2 f(x) 1.5 3 6 12 24 g(x) 1 9 f(x) = g(x) =

A: Given query is to find the the exponential function from the table.

Q: cos4 cos* x

A: Follow the procedure given below.

Q: If g(x) = 3x2- 4x +5 ; G(x)=x3 – 2x2+ 5x , then G is the anitiderivative of f . A) True B) False

A: Let's find. 

Q: Let f(x) = 2x + 2x 5 Use the limit definition of the derivative to calculate the derivative of f: f'...

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Q: at x = 1 and f(1) = 4 at x = 2 andf(2) = 3 10. There is a jump discontinuity 9. There is an infinite...

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Q: (3 +x if x < -1 if -1 sx< 1. (2 - x if x 2 1 Let f(x) = {x2 Sketch the graph of f. y y 3 -3 -2 -1 1 ...

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Q: Given a right triangle. The hypotenuse is 5, the two sides are "a" and "b". The angle that is opposi...

A: Given that: Hypotenuse = 5.Two sides are a and b.Angle opposite to side b is 30°.

Q: Which of the following ordered pairs satisfy the 7x+8y0? а. (1,-5) b. (5,-1) . с. (1,1) • d. (0,0)

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Q: Find the general solution of the given higher-order differential equation. d³u d²u 2u = 0 dt3 dt2 u(...

A: Given that: d3udt3+d2udt2-2u=0

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A: Given that: 1. y=2x2-3x+1      at (-1, 6)2. y=x2+x+1           at (-2, 3)3. y=3x2-x+1      at (1, 3)...

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A: Here we will find how fast is the balloon rising,

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Q: 2 50 = 50t Rint 204 Rint %3D

A: Solving the problem by finding the Rint.

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Q: Find values of C1 and C2 so that the given functions will satisfy the prescribed initial conditions ...

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Q: Evaluate the definite integral. (x – 4)° dz =

A: We just have to rise the power of (x-4) one more than the existing and divide by the same than apply...

Q: Let F(x) = f(xº) and G(x) = (f(x))® . You also know that a = 12, f(a) = 2, ƒ'(a) = 15, f'(a") = 5 Th...

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Q: 3. Find the general solutions rounded to two decimal places for each of the following. For each ques...

A: Given :a) sin 3x= 0.72sin 3x = 12The General solution is x=(8n-7)π2∪(8n-5)π2  ∀n∈ℤ  

Q: 4 -2 -3 -4 -6구 The graph above is a transformation of the function f(x) = |x| Write an equation for ...

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Q: Use the Chain Rule to evaluate the partial derivatives and dv ди se se at (и, v) %3D (-3, -3). f(x, ...

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Q: In this calculus problem, verify that f has an inverse function. Then use the function f and the the...

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Q: Evaluate the following integrals using “Integration by Substitution”.

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Q: Find the limit. (If the limit is infinite, enter 'o' or '-', as appropriate. If the limit does not o...

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Q: Evaluate the integral. 5n /2 2, 1 - cos t dt 3π/2

A:     ∫3π25π21-cos2tdt=∫3π25π2sin2tdt=∫3π25π2sintdt=∫3π22π-sintdt+∫2π5π2sintdt=1+1=2

Q: Calculate the Taylor polynomials T, and T3 centered at x = a for the function f(x) = 19 1n(x + 1), a...

A: Taylor series of function fx at a is defined as:       fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…=0+ddx...