I. Evaluate the following limits x-tanx 1. lim x-sinx x-0

Q: III. Directions: Find the derivative of the given functions with respect to x using the limit…

A: i) f(x)=3x2+5x-7ii) fx=12x2-9x

Q: Problem Revolve about the (a) x-axis and (b) y-axis the area enclosed by y² = x and y=x³.

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Q: -.f x³ ex² dx 3

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Q: A particle is moving along a horizontal line such that its velocity in m/s is given by v(t) = 2t²…

A: A particle is moving along a horizontal line such that its velocity in m/s is given by vt=2t2-16t+30…

Q: Find the Integrating Factor (I.F) of the following linear differential equation: (1 + ²) + y = t…

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Q: What is the center of gravity of the solid formed when the plane region bounded by 2x+y-2= 0, y = 0…

A: Center of gravity is given.

Q: A real estate firm estimates that the value of a certain property will be given by the function 517…

A: To solve the following problem

Q: Perform the integration. 3 (13 (|3* − 1| + |3* − 3|) dx 0

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Q: (x² - 12x + 9) dx (x²-3x + 2)² 2. √(x²

A: Given: I=∫x2-12x+9x2-3x+22dx   As we know that; The Power Rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: A company manufactures two products, A and B. If x is the number of thousands of units of A and y is…

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Q: Find the capital value of a fort at a strategic location, where the annual rent is $750,000, paid in…

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Q: x² + x 1. lim x++∞ e²x + Inx 2. lim (sech 2x) esch x² +0+x

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Q: Find all points where the given function has any local extrema. Identify any saddle points. f(x,y) =…

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Q: 1. Let B = {. What is A. C. B. ( D. cannot identify } and the operation * is defined by the table…

A: To find what element we get after operating the given elements.

Q: Find I must find the indefinite integral then I need to use the result to calculate the definite…

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Q: Evaluate the limits using the L'Hopital's lim (tan x) (sin x-1) x+2+

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Q: T Evaluate sec²20d0 a. 00.33 b. 0.5 c. 0.67 d. 0.25 e. NONE OF THE ABOVE O A OB O O D OE

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Q: 7. Find the mean of a student's test scores if he earned 95, 93, 85, 90, and 91 points on five…

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Q: Find the derivative of the function. s = t In |t| ds dt 11

A: The objective is to find the derivative.

Q: A kite flying 80m high is blown horizontally by the wind at a velocity of 5m/s. If the string is…

A: We are given that a kite flying at 80m height is blown horizontally by the wind at a velocity of…

Q: Perform the integration. x-1 dx x² + 5x + 8

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Q: Perform the integration. TT 3 sec³x tan x dx 2 + sec x 0

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Q: 5. Find the Maclaurin Series for f(x) = e²^²+ex 2

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Q: Question 2 A piecewise function is defined as f(t) = {2t²-4 3 0 ≤t<5 t25 i. Sketch the graph of…

A: Explanation of the answer is as follows

Q: What is the second derivative of y = 6x² 3x³ + x² - 5 ? - Oy"= 72x² 18x + 2 Cinema) Oy" 24x³9x² + 2x…

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Q: -0.03t The function f(t) = 9000 e represents the rate of flow of money in dollars per year. Assume a…

A: Given that,

Q: Use the Second Derivative Test to find all relative extrema. (a) h (x) = x - 2 cos x, [0, 4π]

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Q: Given: zi = 2215° evaluate z and express the result in the Cartesian form. (Answer: j64)

A: Using De moivres theorem

Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

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Q: (6) Sketch a graph of a function, f, that has the following properties: • lim f(x) = 3 and lim f(x)…

A: Given information:  ----------------------------------------------------------------------------…

Q: TU Evaluate a sec²20d0 8 a. 00.33 b. 0.5 c. 0.67 d. 0.25 e. NONE OF THE ABOVE

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Q: Electric usage over the course of a day varies. The graph shown is of electricity costs per hour.…

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Q: Suppose that a movie theater has a screen that is 29 feet tall. When you sit down, the bottom of the…

A: Given: θ=Viewing angleθx=tan-137x-tan-18x…

Q: 2. Find each of the two areas bounded by the curves y = x³ - 4x and y = x² + 2x

A: Given problem:- Find each of the two areas bounded by the curves y = x3 - 4x and y = x2 + 2x

Q: What is the x-coordinate of the centroid of the plane region bounded by the x-axis and the…

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Q: Perform the integration. 3 [² (13² - 11 + 13* - 31) dx

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Q: too (-1)³²x²² 4) Let sinx= -1=0 2ntl a) Find a power series for xsinx b) Differentiate the power…

A: Here is the solution:

Q: Let f(x) = e2sinx 1. Find the absolute extremum values off on the interval [7]

A: To find the extreme values of given function at given  interval.

Q: A small business determined that the price-demand and cost functions for producing and selling x…

A: We have to find the marginal profit.

Q: In a certain country, the number of people who drive electric vehicles can be mod the function P(t)…

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Q: Convert each degree measure to radian measure as a multiple of . Do not use a calculator. (a) 135°…

A: We know that for converting degree to radian , we multiply by factor π180° Therefore

Q: What is the center of gravity of the solid formed when the plane region bounded by 2x + y -2= 0, y =…

A: The given region is as follows: Now, rotation of the bounded region about y-axis will result in a…

Q: II. Evaluate the following integrals. 4. J 9x² 9x → 5 - 18x + 13 - dx

A: A detailed solution is given below.

Q: The following differential equation is a Bernoulli equation: 2 dy + 27/ y3 where y = f(t) dt By…

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Q: 1-) x ² ( xdx tydy) = (x² + y²) dx ; x =1 when y=2

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Q: quickly

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Q: Problem 7. Find the limit lim f(x), where 2--2 x²-4 2+21 x-2

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Q: The integral of 3^4x dx is equal to * O 4^4x / In3 + C O 3^4x/In12 + C O 3^4x / In27 + C O 3^4x /…

A: SOLUTION-

Q: 1.) +y=e+ dx=3e-t 2. .) d- given: x(0) = 0, y(0) = 1 dy-x=0 d+y=1 given a z (0) = -1, y(0) = 1.

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Q: For which values of n is the function ya solution of the differential equation xy"-Kxy'-6y=0

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