Show that y = - In x + 4x-2 is a solution of y'' - 1 = 0.

Q: Use the Divergence Theorem to calculate the surface integral JI F(x, y, z) = 3xy²i + xe²j + z³k, S…

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Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by given…

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Q: If 3 ["* f(2)dx = [*, f(2)dx + ſ,” f(x)dx - [*ª* f(x)dx, -7 2 -7 what are the bounds of integration…

A: If , then to find the bounds of integration for the first integral.

Q: In 2D, which pair of lines are parallel? O A) x+ 7y-2 = 0 and 7 = [2,5] + s[1,7] B) 3x-4y - 2 = 0…

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Q: Provided below is a differential equation: y"+7y'+12y = 80e^(-x) Utilize the method of undetermined…

A: the differential equation given is

Q: Find dx dt dy dt 히 dx dx dy dt dt = || dy dx x = 5t - 5ln(t), = and y = 6+² 6t-2

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Q: Find k such that the function is a probability density function over the given interval. Then write…

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Q: 9 d²y dx² 30 € dx + 30 dy dx + 25y = 0; when x = 0, y =0 and = 2

A: we have given differential equation with initial condition

Q: Identify all the possible values for A in the following equation that would make the conic section a…

A: We have,   Ax2 - 3xy + 4y2 - 5 = 0 - 3xy + 4y2 - 5 = 0

Q: The graph shows one of the six basic functions and a transformation of the function. Describe the…

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Q: The polynomial of degree 5, P(x) has leading coefficient 1, has roots of = multiplicity 2 at x 3 and…

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Q: Use the graph off to complete parts (a) through (1). If a limit does not exist, explain why. 8- Ау…

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Q: Find the volume of liquid needed to fill a sphere of radius R to height R/5 The answer I have is…

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Q: The perimeter of a triangle is 52 in. The shortest side is 7 in. less than the longest side. The…

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Q: Evaluate the triple iterated integral. 255 2 2 X 4 xyz³ dx dy dz

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Q: Aiming the Communication Device You reach the communication device and are alerted by your computer…

A: The equation of the force field of the device:Since the communication device has to be taken to the…

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: The number of franchises for its products will grow at the rate where t is the number of years, 0 ≤…

Q: dy Write the function below in the form y = f(u) and u = g(x), then find as a function of x. dx y…

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Q: Write the equation y2 - 12y - 8x+ 20 = 0 in vertex form. O (y + 2)² = 8(x-6) (v+6)² = 8(x-2)

A: Given Equation

Q: Problem 2. Let f(x) be any differentiable function. Prove the below formula, using a substitution.…

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Q: A person's Body Mass Index is I = 2, where W is the body weight (in kilograms) and H is the body…

A: I have appended the formula used in the solution procedure part

Q: Find an equation for the graph sketched below f(x) = 8+ 74 -5-4-3 -2 -I 65 5₂ I 3 2 1 my na mg -1 -3…

A: Using a base function and graph, we can solve the question.

Q: The velocity function for a particle moving along a line is given by v(t) = -t² + 5t - 6 cm/s. Find…

A: Given that,Velocity function is,v(t) = - t2 + 5t - 6   and interval is = [-3, 5]we have to calculate…

Q: Suppose that f(x, y) = y√√√x³ + 1 on the domain D = {(x, y) |0 ≤y ≤x≤1}. D + Then the double…

A: We have to evaluate the double integral.

Q: Evaluate the following integral using the fundamental theorem of calculus. Sketch the graph of the…

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Q: 5. Consider the function f(x) = tan r, -T/2<x<T/2. (a) Use the quotient rule to find an equation for…

A: The slope of the tangent to the curve y = f(x) at (0, 0):The quotient rule:Using the quotient…

Q: Use f(x) = x²/3(x - 5) and its derivative f'(x) = 5(x - 2) 3x1/3 to find each of the following. Find…

A: Given that a function f(x) = x2/3(x-5).And we find critical points.

Q: Determine whether the geometric series is convergent or divergent. If it is convergent, find the…

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Q: Your friend comes up with the following function for her roller coaster prototype and does not…

A: Graph should have three extrema and two points of inflection. So the graph is drawn below to meet…

Q: A box with an open top has a square base and four sides of equal height. The volume of the box is…

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Q: 4. Let f(x) = √√x+1 if x<3 5-x if x ≥3. Determine the one-sided limits as x approaches 3, and…

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Q: If h(x)=√ 7 + 6f(x), where f(1)= 7 and f (1)= 2, find h(1). h'(1) = x

A: Given function Where

Q: Eloise needs to finish a 516-page report on international trade so she can present it at the big…

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Q: Use linear approximation, i.e. the tangent line, to approximate 8.3 as follows: Let f(x)=x. The…

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

Q: Find the critical points e for the function f and apply the Second Derivative Test (if possible) to…

A: We have to find the critical points and find if the points correspond to local minima or…

Q: The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure…

A: The volume  of an ideal gas varies directly with the temperature  and inversely with the pressure .…

Q: a. x = 2y, y = 2 and y= 3; revolved about x-axis 4. (0, 3) y=3 (0, 2 y=2 -2. -4. 0 x=0 x = 2y + 2.…

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Q: A cyclist rides west for 7 mi and then north 14 mi. What is the bearing from her starting point?…

A: The bearing is the angle between the line connecting the starting point to the end point and the…

Q: Determine whether the following equality is true or false. 3 fff(x,y) d4 = [³ f√/18-²f(x,y) dy dx, D…

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Q: Evaluate the integrals that converge, enter 'DNC' if integral Does Not Converge. 7x (x²+4)² [x da

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Q: A particle moves in a straight line with velocity t-2 - ft/s. Find the total displacement and total…

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Q: Evaluate the following improper integral if it is convergent. 0 S (4e³x) dx

A: given integration

Q: Points A and B are separated by a lake. To find the distance between them, a surveyor locates a…

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Q: 2-√√√1-x Evaluate: lim x+3 OA) 2/1/20 O B) // E-+-% ○ C) 1 O D) undefined

A: The given limit is

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

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Q: 5 25 Determine if the vectors b= i+ = 2 b and a are (Choose one) orthogonal parallel neither 5 ---/1…

A: To determine whether the vectors   and  are orthogonal, parallel, or neither.

Q: What is the slope of the tangent line to the graph f(x)=x-√√x-1 atx=5? O A ) =// B) = C) 3/ OD) 4

A: Given

Q: x² (x³ – 6)³ This can be transformed into a basic integral by letting Consider the indefinite…

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Q: Find the minimum and maximum values of the function y = critical points and endpoints. (Use decimal…

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Q: Problem 4. Consider the integral x³ x² +9 J (a) According to lectures, which substitution should we…

A: As per our guidelines we can answer only 3 subparts of the given question so kindly repost the…