A rectangular piece of cardboard has a size of 45 x 24 cm. This cardboard will be made into a box without a lid by cutting the four corners into a square and fold it. Determine the size of the box so that the volume of the box is maximum.

Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series…

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Q: Each of the regions A, B, and C enclosed by the graph of f and the x-axis has area 6. Find the value…

A: Answer and explanation is given below...

Q: tan-x dx 3+3x? -1 (b). /

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4 - x from above inside x = y2,x = 4.

A: Answer is in step 2.

Q: 3-x QI) Evaluate the integral S* dy dx using polar coordinate

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Q: 3. Determine the following a A negative angle in radian measure coterminal to Show calculation steps…

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Q: Consider the following function and dosed interval. fx) = x2/3 - 1, [-27, 27] Is f continuous on the…

A: F(x) is not differentiable on (-27, 27)

Q: E) INTEGRAL : 9.) S(5t3 + 2t? – 5t – 50)dt 10.) S(3x2 + 2x + 500)dx

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Q: Sketch the region in the plane consisting of points whose polar coordinates satsfy the given condi-…

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Q: Find a polar equation for the curve represented by the given Cartesian equation. 9. a? + y? = 25

A: Given equation x2 + y2 = 25 To be found : Polar form.of given equation.

Q: xsin(x³) dxdy

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Q: x² +64 Using trigonometric substitution, given dx, the simplified form of the integral is= sec ede…

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Q: Consider a continuous function f(x). The function has critical points at x = -7, x = -2, and x = 7.…

A: f(x) has critical points at x=-7 , -2 , 7Since f''(-7), f''(-2) is positive ⇒There is local minimum…

Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations…

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Q: Find the equation of the tangent line for x=t^3+1, y=t^2-t at t=1

A: x=t3+1  y=t2-t To be found - Tangent line equation at t=1

Q: 22n Σ (2л — 1)". - Vn² + 1 3 n=1 Use limit comparison test to show that the given power series is…

A: Solving

Q: Find the distance between the parallel planes 10х — 5у — 52z — 26 — 0. 2х + у + 2 %3 0 and - - NOTE:…

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Q: full

A: We have to determine the given series is converges or diverges according to the given information

Q: /2n?

A: The given series is: ∑n=1∞(-1)n(-1)n2n2+5=∑n=1∞(-1)2nn2+5n2=∑n=1∞1n2+5n2

Q: п(х — 2)" 3" (2n – 1)3* VI. Consider the power series n=1 a. Show that the power series converges…

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Q: determine if the series diverges or converges

A: This question can be solved using the concept of convergence and divergence.

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 6z + 18 =…

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Q: Consider the tollowing Maclaurin series: (-1)"x2n (2n)! COS X = for all x e R. n=0 1. Let f(x) =…

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Q: 4. Find the Laplace transforms of the functions: (a) f(t) = t² (b) f(t) = t – 2e3t

A: a) f(t)=t2b) f(t)=t-2e3t

Q: Determine if the improper integral (1 e" )2 dx converges or diverges. If it converges, find its…

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Q: Consider the tollowing Maclaurin series: (-1)"x²n (2n)! CoS X = for all x E R. 1. Let f(x) =…

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Q: V9 – 4x2 Evaluate: A f (x) = V9 – 4x2 + 2 sin () + C V9 – 4x2 – 2x sin- () + C B 6/ | | f (x) = f…

A: For the solution follow the next step.

Q: X In Зх +1 y y' X

A: Given ; ln(x2/(3x+1))=y/x.

Q: 3. (2x - 2)dx

A: Follow the procedure given below.

Q: Given the set of parametric equations x = 2t2- 1 and y = 3t + 4, eliminate the parameter t and…

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Q: Determine if the improper integral converges or diverges. Find its value if it converges. Show…

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Q: 5. Evaluate f V2x + 1 dx. (2x + 1)/2 + C a. 3. b. (2x + 1)/2+ C c. (2x + 1)/2 + C d. (2x + 1)/2 + C

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Q: d -sin 6 if0 is given as dx What modifications would have to be made to find the derivative an angle…

A: We have to find derivative of given function.

Q: Is the vector projection of B onto A, perpendicular to B? Is the angle between projAB and the vector…

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Q: Which of the following is the general solution of the separable equation, dy/dx = 12x³y? A. y =…

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Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series…

A: For radius and interval of convergence we will first findlimn→∞an+1an then equate it to <1 and…

Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

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Q: 1. Evaluate the following integrals. 1 1. -d.x J #(9 – In² x)5/2" |

A: Follow next step

Q: 6. Use Laplace transforms to solve the initial value problems: (b) x" – x' – 2x = 0; x(0) = 0, x'(0)…

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Q: From Rogawski ET 2e section 10.3, exercise 5. Use the Integral Test to determine whether the…

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Q: Question A 5-foot ladder is leaning against a wall. If we push the ladder toward the wall at a rate…

A: let x be the distance of bottom of ladder from the wall andy be the distance between top of the…

Q: Question For the equation given below, one could use Newton's method as a way to approximate the…

A: This question is related to numerical methods, we will solve it using given information.

Q: 24 3y7 ts dy

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Q: Question Using Rolle's theorem for the following function, find all values c in the given interval…

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Q: X+ 1 Evaluate lim x→1* ** - 5x +4• | O-1 OO OO

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Q: ind the point of intersection (xo, yo, zo) of the lines given as: L: x = 2 + t, y= 4+5t, z = 5 +t L:…

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Q: [ sec" x (Vtan' x+ 1) +1) dx 2. 4 sec'x 3

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Q: 10. [ tan 0 de 12.f cos do 3

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Q: A firm produces two types of calculators each week, x of type A and y of type B. The weekly revenue…

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Q: the Q2, Find hergth of o polor Curve ア= B4 Use this formula dr de

A: Given:  The polar curve is given byr=eθ2 To Find:  To find the length of the given polar curve by…