1. The function is given piecewise: ƒ(x) = cos(x) 0 X if x < 0 if x = 0 if x > 0

Q: 6. Suppose that a. 6 b. 2 a b - 3c = 0 → → and a c= 2. What is a C. -6 d. -2 → b equal to?

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Q: Evaluate the integral. If the integral converges, determine the number it converges to. If the…

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Q: (b) J₁ In x x3 dx

A: To determine whether the following integral is convergent  or divergent.  ∫1∞lnxx3 dx Note: Since,…

Q: The Seventh Gate As you approach the seventh gate, you notice that it is only a short distance to…

A: Given:  fx=2-62x To Find:  To determine the domain of the derivative of fx and  then to evaluate it…

Q: 10. Solve and check by integrating factor: {Integrating factor e[2(=)α = } y '+ 2 y = 4

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Q: 5 430 X 32°

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Q: = x³ and What is the volume of the 3D region, whose base is the region between the curves y = y = √,…

A: We have,   Curves :- y = x3 and y =  √x  Cross section are squares.

Q: Find an equation of the plane passing through the three points given P = (4, 2,9), Q = (6,7, 18), R…

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Q: For each of the following infinite series, determine whether the series is absolutely convergent,…

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Q: I. Determine if the differential equations are linear or non-linear. 1. y'-(sin x)y=e* 2. y'- y² = x…

A: NOTE: Refresh your page if you can't see any equations. . The standard form of the first-order…

Q: For an object whose velocity is given by v(t) = - +4, what is its displacement on the interval t = 0…

A: Given that valocity v(t) = - t2 +4. And interval is t=0 to t=3. We find displacement on this…

Q: f(x) = 1 1+4x2

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Q: 7. Use the convolution theorem to find the inverse Laplace transforms of: 1 (a) F'(s) = (²+9)2 1 (b)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 3. Evaluate: 5x² - dx {2 Decimal places} Type. U = S

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Q: 10 2 dt √ 4 + t²

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Q: Solve the equation for n ny+ zp=nq+h

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Q: In Problems 1-5, let R be the region bounded by y=x² + 3, y = 2x, x = 0, and x = 4. Each problem…

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Q: a⃗ =⟨2, −3⟩ and b⃗ =⟨1,4⟩​. Represent a⃗ +b⃗ by using the parallelogram method. Use the Vector…

A: vec a = &lt; 2, - 3 &gt; vec b = &lt;1, 4 &gt; to evaluate and draw  vec a + vec b by parallelogram…

Q: Write the following numbers in Cartesian form (i.e., in the form a + bi). Use the principal value…

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Q: 7. Given a= [-1, 2,6], b= [0,-1, 3] and c= [2, 4, 5]. Determine a xb.c

A: we are given 3 vectors a, b and c and we need to determine axb.c the vectors are given as--…

Q: 7. A lidless large steel fuel tank is cylindrical in shape. To optimize storage in the truck, the…

A: A lidless large steel fuel tank is cylindrical. To optimize the truck, the total volume of the…

Q: Sketch a continuous curve for which each of the following statements is true. f(-1)=0, f(0) = 2,…

A: According to question,Given conditions,f-1 = 0,f0 = 2,f1 = 4,f'-1 = f'1 = 0,f'x &lt;0 for the…

Q: 1. In three-space, find the intersection point of two lines ₁ = (−1,1,3) + t(1,2,-2) and r₂ = (5,3,…

A: The point of intersection of two lines is a common point on both lines, it has same x,y and z…

Q: 7. Use the D-Test to Find the relative extrema and or saddlepoints for the function: f(x, y) = 3xy —…

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Q: Evaluate the integral. TT/2 [*¹²7 cos²(0) do de

A: NOTE: Refresh your page if you can't see any equations. . use the formula: cos2x=1+cos2x2

Q: 3) Find the equation of the osculating circle of the standard parabola y = x² at its vertex.

A: To find the equation of the osulating circle of standard parabola y=x2 at its  vertex

Q: Use the slope-intercept form to write an equation of the line that passes through the given point…

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Q: What present value amounts to $358,312.09 if it is invested for 5 years at 16% compounded…

A: What present value amounts to $358,312.09 if it is invested for 5 years at 16% compounded…

Q: Intervals on which the function is increasing and intervals on which it is decreasing, ● critical…

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Q: Use partial fractions to find the area of the given region. 12 x + 5x + 6 y -1 y 3 2 1 -1| 1 2 3 4 5…

A: The region is bounded by the curve y=12x2+5x+6 in the interval 0, 4. To find the area of the region…

Q: What is the area between the curves y = -²³ and O 10 -24

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Q: 3. Use the Fundamental Theorem of Calculus Part I to determine the derivatives of the following: (i)…

A: We need to solve Integral problem.

Q: 4 3 -3 +---)-(6) --- 00 0 12 0 A-1 = 120 A-21= 0 5 3 0 0 0 3 3 -3 -(6)-( 0 -1 0 1 2 -1 1 0 0 1 0 0 0…

A: ⇒A-I=43-3000120 ⇒A-2I=33-30-1012-1 ⇒A-4I=13-30-3012-3

Q: Graph the function and find the limit (if it exists) when x approaches 2. [2x + 1, x < 2 x + 3, x ≥…

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Q: A data-recording thermometer recorded the soil temperature in a field every 2 hours from noon to…

A: We need to find average temperature.

Q: 1. A table of values of an increasing function f is shown. Use the table to find lower and upper…

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Q: Integrate by partial fractions: x² - 4x + 4 r(r - 1)³ -dx

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Q: In(1 + √x) √x s dx

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Q: Find a plane containing the point (5,-2,8) and the line of intersection of the planes 7x+6y-z = 27…

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Q: ∞0 (x+1)" n=1 Vn4n

A: Use the Ratio test

Q: 2. The normal line slope of f(x) = (a - 1)x² + 3x - 2 is GIN at x=-2, a=?

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

Q: Divide. 4+i -2+3i Enter your answer, in standard form for complex numbers, in the box. 4+i -2+3i ||

A: Given

Q: Solve = (x²+6)(y-7), y(0) = 2. dy dx

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Q: In Problems 6-10, let R be the region bounded by the semicircle x =√√4-y² and the y-axis. Each…

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Q: Question 10 Use the graph to estimate the limit of the function shown in blue as x→0. -5 -4 -3 -2 -1…

A: Since you have posted multiple questions i can do first question as per our company guidelines,…

Q: The following table gives the millions of metric tons of carbon dioxide emissions in a certain…

A: (a) To create a linear function that models the given data, we need to find the equation of a line…

Q: Integrate by parts [2x(x-3)* dx Formula: Sudv=uv-fvdu,

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Q: Given one form a line, match it with its equivalent equation in another form. [x, y, z] [3, 2, 1] +…

A: a. x,y,z=3,2,1+t1,2,3b. x,y,z=-1,0,1+t0,1,0c. x,y,z=1,2,3+t3,2,1d. x=0y=1z=te.x=-ty=1z=1+t

Q: Solve the following differential equation y"+y' = sec(x).

A: We have,     y'' + y'  = sec (x)

Q: What is the partial fraction decomposition of the function O x+1 x² 1 2x -x-2 2(x²+4) 1 x² x+2…

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