Solve the initial-value problem. x' + 7x = e-7t x(t) =| X cos(t), x(0) = -1

Q: Find the number a such that the line x = a divides the region bounded by the curves y = x, y = 0,…

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Q: Evaluate: lim (x² + €¯²) (x²¹ cscx) I→0+

A: We will evaluate the given expression using DL hospital rule.

Q: Find two positive real numbers such that the sum of the first number squared and the second number…

A: Convert it in one variable then use double derivative test

Q: A manufacturing company has determined that the cost (in pesos) of producing x units of a product is…

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Q: 4. Evaluate the double integral: L Later y¹/3 x² +1 (Hint: Change the order of integration to dy…

A: Given: I=∫08∫y132yx7+1dxdy The region bounded by the curves x=y13, x=2 from y=0 to 8.

Q: the graphs of y=2x^2 and y=mx -2 intersect at the points A and B. The point B has coordinates (2,8),…

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Q: 2. If ƒ (x) dx = = 4 and 3g(x) dx = −9, evaluate [*² [3ƒ(x) + g(x)] dx -2

A: Topic = Integration

Q: lim 4 į (( #)² + ¹); n n

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Q: Cπ/2 sin² 3x dx

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Q: Consider the following pattern 9 * 1 - 1 equals 8 9 * 21 - 1 equals 188 9 * 321 - 1 equals 2888 9 *…

A: Concept: Inductive reasoning: Inductive reasoning is an approach for arriving at inferences by…

Q: 9. Find the volume of the solid obtained by rotating the region R enclosed by y = -x² + 6x-8 and y =…

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Q: 4e2x S sin(e²x) dx

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Q: d/dx [x/(x^2 + y^2) ] = * O [(y^2 + x^2)/(x^2 + y^2)^2 ] O -[(y^2 +x^2)/(x^2 + y^2)^2 ]…

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Q: Evaluate the double integral: y SLAZ+1 y²/3 x + 1 (Hint: Change the order of integration to dy dr.)…

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Q: Identify the surfaces of the following equations by converting them into quations in the Cartesian…

A: To identify the quadratic surface of the equation: Given: The equation of the surface is r=z2-1.…

Q: Write and evaluate the definite integral that represents the area of the surface generated by…

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Q: Find all solutions of the equation in the interval [0, 27). 2 cos 0+1=0 Write your answer in radians…

A: Given:   2cosθ+1=0   2cosθ+1-1=0-1             {subtract 1 from both sides}   2cosθ=-1   2cosθ2=-12…

Q: Given that v = ⟨0, –2⟩ and w = ⟨5, –8⟩, what is w – v?

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Q: Find the value of c so that the domain of f(x) = √c - x² will be [-5,5].

A: The function f(x)=c-x2 has the domain -5,5

Q: Use mathematical induction to prove the following: 1 + 3 + 5 + ... + (2n – 1) = n² for n ≥ 1

A: This question can be solved using the four basic steps of mathematical induction.

Q: Let f(x) be a function which has inverse. If f(3)=8 then f-1(8) equals a. 8 b. -5 c. 5 d. 3

A: It is given that,  f(3)=8 f-1(8)=?

Q: Let F be the function below (Click on graph to enlarge) Evaluate the following expressions. Note:…

A: limx→a F(x)=L if and only if limx→a+ F(x) = L= limx→a- F(x) . A function F(x) is continuous at x=a…

Q: Evaluate the given function by using three terms of the appropriate Taylor series. 4.3 √4.3 = (Round…

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Q: Find the arc length of the curve x = -2y³/2 from y = 0 to y = 10. Length =

A: Solve the following

Q: J 7+6x - x²dx

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Q: Let f be the function below. You can click on the graph to get a larger image. M Determine the…

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Q: Find the equation of the tangent plane to the surface defined by the function f(x, y) = x³…

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Q: Q2/ prove [A] [A] = [I] if [2 4 -5 [A]= 2 7 1 3 4

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Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

A: Converting into Cartesian form

Q: 5. Use Cartesian coordinates to evaluate If ₁² dv D where D is the tetrahedron in the first octant…

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Q: Evaluate the double integral: 2 So de dy. Sola 0 Jy¹/3 Y x7 +1 (Hint: Change the order of…

A: Application of integration

Q: Find the area of the surface obtained by rotating the curve from x = 0 to x = 5 about the x-axis.…

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Q: 1) A pump is used to fill an inflatable mattress at a constant rate of 0.25 cubic feet per second.…

A: As per bartleby guidelines we only give first question answers.

Q: (a) Find (in terms of m) lim f(x) z--1¹ Limit= (b) Find (in terms of m) _lim_ f(x) Limit= (c) Find…

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Q: estions 14 refers to data given below A certain radioactive material is known to decay at a rate 1…

A: Given problems:- A certain radioactive material is known to decay at a rate proportional to the…

Q: Watch the video and then solve the problem given below. Click here to watch the video. Find a…

A: -1 as a zero of multiplicity 3, 0 as a zero of multiplicity 1 and 1 as a zero of multiplicity 1.

Q: 4. Letf(x)=x22/5 - 19x². Determine the largest n for which fis n-times continuously differentiable.

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Q: find the integral from 1 to 4 of (3t^(3/2) i+(t+4)(√t)k)dt

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Q: -TL 4.) x² sin(xy) dydx

A: Given ∫0π∫01x2sinxydydx

Q: F = cos(x) Î+sin(y) ĵ+cos(z) k

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Q: The function f(x, y) = x² + y² √x² + y² +1-1' (a) {(x, y) = (0,0)} (b) {(x,y) = R²2} 2 if : (x, y) =…

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Q: Let f(x) = cos z. Determine the z-value(s) where the function has a maximum or minimum value on [0,…

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Q: find the given general differential solution, using homogeneous equations with constant…

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Q: Consider the substitution 1 u(x) y(x)* What is ? Use the substitution to obtain a 1st-order linear…

A: Explanation of the answer is as follows

Q: The director of the school play has to assign 5 lead roles. If the roles are being chosen from a…

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Q: 4. Evaluate the double integral: So SAFI y¹/3 x7 +1 (Hint: Change the order of integration to dy…

A: Graph of the limits÷ x=y13,x=2,y=0,y=8

Q: find the curvature of r(t)=⟨3t2, ln(t), t ln(t)⟩ at the point (3, 0, 0).

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Q: Gradient 3. Find the gradient of the following scalar functions. (c) f(x,y)=at (-1.1) (d) $(x,y,z)=-…

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Q: 2) Find the absolute maximum and minimum for function F(x,y)= 4x³-2x²y+y² on the region R bounded by…

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Q: Suppose that P₂(x) = a + bx + cx² is the second degree Taylor polynomial for the function f about x…

A: We have to find the sign of a, b, c.