42. Given that "sin'x dx-, what is sin¹0 do?

Q: Show that the vector field F = is not conservative by showing it is not path independent.

A: check the conservative of f using curl of F

Q: Given f'(x) = 3x4 — 4x³ + 7. Find all critical numbers of f'. (a.) 1 and 2 (b.) 1 and 3 (c.) 0 and 1…

A: To find the critical numbers of f'

Q: J 4 √ (61 0 (6t - 3) dt

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Q: 5. Consider the tables of values for the two functions shown. X -2 −1 0 1 2 y = f(x) 9 4 1 0 1 X -2…

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Q: Suppose that the demand of a certain item is q = 50e-0.02p. Remember, elasticity is given by the…

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Q: Question 3 What is the form of the particular solutiony for the differential equation y"-y= R(x)…

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Q: 4. Calculate the integral assuming the following: a. f² f(x) dx = 5₁ g(x) dx = 1 5, S² 12 4 fo b.…

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Q: dy Find L y = ln (2²+4) + + Icos HIN

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Q: Which of these vector fields are irrotational? Identify all of those that satisfy this property. A B…

A: The given vector fields, A) u=-x, y, 0B) u=-y, x, 0C) u=-x, z, 0D) u=x, y, z We have to find the…

Q: Solve the inequality |8 − 6x| ≥ 7 and determine the solution set.

A: Given: So,                 8-6x≥ 7⇒8-6x≤ -7  or   8-6x≥ 7⇒x≤16  or   x≥52⇒Solution:  x≤16  or…

Q: A spherical balloon is being inflated with helium at a rate of 201 cm³/min. How fast is the…

A: topic - application of differentiation

Q: Let C be a constant such that the integral converges. Find C and evaluate the integral. C = с -de=…

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Q: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 1 and roots of multiplicity 1…

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Q: Find the sum: 161 6 5 + 2π 5 + 3π 5 + 4π 5 + ... + 23m 5

A: As we know the expression for the sum of nth term of the arithmetic sequence is: Sn=n22a+n-1d Where…

Q: area of the region enclosed between f(x) = x² + 2x + 11 and g(x) = 2x² + x − 1.

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Q: Determine if the vertex of the graph of the equation is a maximum or minumim point. y=x²+4 vertex is…

A: Given query is to find verteyis maximum or minimum.

Q: Question Determine the derivative of the parametrically defined curve represented by the equations x…

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Q: Consider the following initial value problem, defined for t > 0: dy dt a. Find the Laplace transform…

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Q: Use a triple integral to find the volume of the wedge bounded by the parabolic cylinder y=x² and the…

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Q: 35. F(x) = x4/5(x − 4)² 37. f(0) = 2 cos 0 + sin²0

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Q: 4. FIND THE 2ND DERIVATIVE f(x)= (3x²-2)log (3x²-2); x

A: According to bartleby guidelines we supposed to do the first one of multiple questionskindly repost…

Q: 2. (sin 0-2r cos 0)dr + r cos 0(2r sin 0 + 1)d0 = 0 0+

A: Given differential equation ( sinθ - 2rcos2θ )dr + rcosθ( 2rsinθ + 1 )dθ = 0 standard form Mdx + Ndy…

Q: If a 180-mile trip took 7 1/2 gallons of gas, how many miles can be driven with a full tank of 14…

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Q: x² 3 (x³ – 9)³ This can be transformed into a basic integral by letting Consider the indefinite…

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Q: Why does I1 = ln(u) in step three?

A: We have to tell why does  I1 = ln(u) in step 3

Q: re4 1 2 e² x ln²√x dx

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Q: Determine whether the series converges or diverges: Input C for convergence and D for divergence:…

A: The answer is given below:

Q: Use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of f and…

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Q: Some ecologists divided a female bird population into three categories: juvenile (up to 1 yr old),…

A: We have to find the population of birds.

Q: Question Determine the second derivative of the parametrically defined curve represented by the…

A: given  x(t)=2t2-2t+4            y(t)=-8t3+8t2+4t+2dtndt=ntn-1d dt(ab)=bdadt-adbdtb2dydx=dydtdxdt

Q: Find the area of the graph enclosed by y=7x and y=4x2

A: Given:     Curves y=7x                 y=4x2 The area between the curves is the area between a curve…

Q: ΔΔΔΔΔΥ Στο 1-0 DE ६ η + 3η + 2

A: Sum

Q: Consider the function in the graph to the right. The function has a relative maximum of 3 o at x = 0…

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Q: 31 If f(x, y) = e³¹ sin 9y, then fry is given by:

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Q: L₂ (3x + 4) dx

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Q: Given f(x) = ax³ + bx² + 9x + c. Find b so that (2,3) is a point of inflection of the graph of f and…

A: The inflection point of the graph of f is (2, 3). So,                  f''(x)=0 at (2, 3)⇒6ax+2b=0…

Q: Use Stokes' Theorem to find the circulation of F = ( (xy, yz, xz) around the boundary of the surface…

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Q: Determine the projection of the surface - y² = z on the xy- plane? (Hint: z = 0) O One Line O…

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Q: 39. f(x) = x²e-³x

A: 39) f( x ) = x2e-3xfor find the critical numbers f'( x ) = 0

Q: d. f(x) = (2x-3)5 (2x²- e²x)-3

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

Q: a. a₁ = 1, a2 = 2, an=2an 1+3an 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1. Determine whether the following infinite series are convergent: A. n=1 n! (n + 2)!

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Q: What is the antiderivative of dx/((1+x^2)^2)?

A: We have to find the antiderivative.

Q: 2. a) d) 2 9 T 4 b) e) 5 T 4 13 п 4 c) 2TT f) 23 TT 4

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Q: 8 If f(x) = 14 +₁ 7 0 O f(x) 14+ f(r) x", then f"(x) is co

A: Please refer to the image below

Q: 1) Express in cylindrical and spherical coordinate systems. Cylindrical Spherical Coordinates…

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Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 250…

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Q: x + y - 3z = 2 1) Solve the system of linear equations using the inverse matrix (2x + 3y + z = 0 3x…

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Q: Given ƒ'(x) = 3xª − 4x³ + 7. Determine which interval the graph of f is concave downward. (a.) 1<x<3…

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Q: ind the area between y = 12 sin (x) and y = = 12 cos (x) over the interval [0, π] Jse decimal…

A: Point of intersection⇒12sinx=12cosx⇒tanx=1⇒tanx=tanπ4⇒x=π4