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Q: A cubical container that measures 2 inches on a side is tightly packed with 8 marbles and is filled…

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Q: The length and breadth of the floor of a room are 30 feet and 20 feet, respectively. Square tiles of…

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Q: dx Example: Evaluate 3 + sin x + cos x

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Q: Let f be a continuous function on [a, b]. Which of the following statements is false A If k is a…

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Q: 6.(Somewhat tricky) Use an appropriate substitution to solve: (a) dy y + x dx (b) (y³ + y?x) dx – x³…

A: To solve the following differential equation

Q: Consider the function f(x) = x2 - 9 (a) Find the domain of f. (Enter your answer using interval…

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Q: y = 5x – 6 tan x, concave upward concave downward

A: Given problem:- y=5x-6tan(x) , (-π/2, π/2)  Determine the open intervals on which the graph is…

Q: What would happen to the volume of the cone if the radius of its base is tripled and the height is…

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Q: Solve the following items and show your solutions. b.) Identify if the following functions are…

A: 4.

Q: Consider the function y = 5x4-4x3-3x2+8x-12. What is the average value of the function on [-3, 1] ?

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Q: Determine whether P = and Q = are orthogonal vectors. If W = and V =, compute V x W. If W = and V =,…

A: Explanation of the answer is as follows

Q: The Maclaurin series for f(x) = x²e=* is E-o(-1)" xn+2 п! False True

A: I am attaching image so that you understand each and every step.

Q: 2. Evaluate the improper integral. e COs x dx

A: I=∫0∞ e-x cosx dx Integration by parts;Formula:∫(uv)dx=u∫vdx -∫dudx ∫vdx dxu=cos x, dudx=-sin…

Q: Suppose that you have a task of measuring the lengths of a bridge and a rivet and come up with 9996…

A: True error : true value - approximation. True error in Length of bridge: 1000 - 9996= 4 cm

Q: Find the limit. lim V+3

A: Given query is to find the value of the limit.

Q: Solve the following items and show your solutions. b.) Identify if the following functions are…

A: To determine whether the given function is homogeneous or not.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: For the function glven below, use algebra to evaluate the limits lim f( メー→+ lim f(x), and limf(x)…

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Q: Consider the function f(x) whose second derivative is f''(x)=8x+8sin(x). If f(0)=4 and f'(0)=4, what…

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Q: Use the position function s(t) --4.9+ 650, which gives the height (in meters) of an object that has…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: To determine the point of intersection of the given line and plane.

Q: 4. The graph below depicts a function g(r). Its one asymptote is indicated in red: 4 -5 -4 -3 -2 -1…

A: Find your answer below

Q: 5(3х-1) dx sec ( 3x²-2x)

A: On doing integration we will get

Q: Direction: Solve the following equations using separation of variables. 3. 2xy + 6x(x² – 4)y' = 0…

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Q: 2. y = loga(x³ + 2x – 2) 3. y = In³ (x + sin x) %3D 4. y = tan¬1(3x)

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Q: 2. Solve the given the equation using the integrating factors found by inspection. [2х + усos(ху)jdx…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, -2) Vw(10, 5, -2) =

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Q: 1. 9. 2

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Q: 11 2

A: We can solve this as follows:

Q: Calculate L4 for f(x) = 24 cos () %3D L4

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Q: Determine the horizontal asymptote of the function. If none exists, state that fact. f(x) =5 e 4x…

A: Given function is: f(x)=4e4x

Q: In xdx

A: Formula:Integration by parts:∫ uv dx =u∫v dx -∫ dudx∫vdxdxI=∫ x5 ln x dxu=ln x, dudx=1xv=x5I=ln x ∫…

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers…

A: To find the parametric equation of a line that passes through (-1, 4, -6) and is parallel to given…

Q: A ball is thrown vertically upward. Its height h feet after t seconds is given by the formula…

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Q: EVAUATE FL) OF TRE DIFF ERENTIAL EQUATION AT zEto NITI AL CONDITONE. oit

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = Y, (1, 8, 8) 10…

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Q: Find the dot product of v and u and determine if the vectors are orthogonal. a. v = , u = The…

A: There is more than 1 question, as per the Q&A guidelines we are answering the 1st question. If…

Q: What is the edge of a cube whose volume is equal to that of a rectangular bar measuring 100 cmlong,…

A: Let the edge length of the cube be 'a' units

Q: onsider the following planes. -4x + y + z = 4 12x – 3y + 4z = 16 a) Find the angle between the two…

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Q: Solve for the following application of first order differential equations. Show your solutions. 3. A…

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Q: de

A: The given indefinite integral is: I=∫16θ2-9θ4dθ Taking θ2 as a common in the numerator,…

Q: Consider the function f(x) = x/3(x + 2)2/3 whose domain is (-∞, o). (a) Find the intervals on which…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: Evaluate by using homogeneous D.E. 3 (3x? + y) dx – 2xydy = 0 03 In(x2 + y?) + 4 = C O a = C(9x³ +…

A: To evaluate by using homogeneous D.E.33x2+y2 dx-2xy dy=0

Q: What is the lateral area of a cylinder with a height of 7 cmand diameter of 240 mm? 3360π cm2 1680п…

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Q: Which of the following is NOT a solution to the trigonometric equation 2 cot 0 cos 0 – cot 0 = 0? 2…

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Q: Find the distance between the point and the line given by the set of parametric equations. (Round…

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Q: If f (x) 2e²x Then compute f" (0) + 2f' (0) + 2ƒ (0)

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Q: dm 1-n3 Find if m = 4 In dn 1+n3 dm n6-1 dm 12n2 %3D dn 12n2 dn 1-n6 Option 4 Option 1 dm 12n2 dm…

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Q: Use vectors to show whether or not the points form the vertices of a parallelogram. (1, 1, 3), (4,…

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