Exercises :- Calculate the following limit statements 2 1)lim (tanx) cos x²-sin²2x 2) lim x-0 x2 3) lim(x-1)-¹Inx 4) lim(1 + x) csex x-0 COSX+1 5) lim sin* (x) 1 0cosr 1 6) lim X-7 sinx 7) lim cotx + esca 8) lim(1 X-R 1 sinx 9) lim 10) lim 1-cos2x X- :--) sinx-cosx It

Q: y" — 5y' = x − 2, when x = 0, y = 0, y' = 2

A: To find the particular solution for the given DE.y''-5y'=x-2, when x=0, y=0, y'=2

Q: Direction: Use substitution rule to evaluate the following integrals. COS X 1. S dx 2x 1+x² 3. f- dx…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Differentiate with respect to t. y = d cos(t) + t² sin(t) y'- sin d( 2t + d) + t²cos (t)

A: Given problem:- Differentiate with respect to t.   y = d cos(t) + t2 sin(t)

Q: If f(x) = x'ex, find f'(x) and f'(1).

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Q: A- Find the averag value of the function f(x)=x+ B- Find the aree √x²+2x on(2,4).

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Q: 3. y² = -x, x² + 3y + 4x+6=0

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Q: 3. (x² - y²) dx + xy dy = 0

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Q: Let L(x) be the linearization of the cube root function at x=8. When using L(x) to approximate the…

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Q: SUBJECT: DIFFERENTIAL CALCULUS NOTE: Make the solution detailed and clear in a sheet of paper.…

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Q: For the given function, find (a) the equation of the secant line through the points where x has the…

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Q: Differentiate the function. y = (2x-5)³ (5-x4) 4 dy dx

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Q: The height of a rider on a Ferris wheel is represented by the equation below. h (t) = 62 +45…

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Q: 3 п 2 2 cos² 4x dx

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Q: given value of x. Show your complete solution.

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Q: 5. How is -28 can be express as rational number with numerated the number 4? 84

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Q: J 2+2 cot (2²+42 - 3) -dz

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Q: Given than [(x) f(x) dx = 7 and f (x) da = -5, which of the following is NOT TRUE 6 ® [f(x) dx =…

A: Given that ∫-23fx dx=7 and ∫36fx dx=-5, then to determine which of the following is not True.A…

Q: Wheat is poured on the ground at the rate of 12 cu. ft/sec. The pile forms a cone whose altitude is…

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Q: C. Graf the function of y-5x" if n=3 1. O 1 O 2 2. yax' LEVIC

A: Given data Graph the function y=5xn Where , n=3

Q: S sec³ x+esin sec x - dx

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Q: SUBJECT: DIFFERENTIAL CALCULUS NOTE: Make the solution detailed and clear in a sheet of paper. 1.…

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Q: Determine if the series converges or diverges Sum n=1 (n+1)/(n+3) State the test used, show that all…

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Q: t = 3 ds ml

A: Solution of the problem as follows

Q: Applied Optimization Problem 1. You need to construct a fence around an area of 1600 ft. What are…

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Q: Determine the intervals on which the function is concave up or down and find the points of…

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Q: Is it possible to solve it without a pocket calculator ??

A: Here to evaluate: t=∫03ds(2.78s+0.8s3)12 The integral can't be evaluated manually.

Q: use differentials to approximate the value 1. 664 .05 2. e^0.99 3. square root of 101

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Q: T/F: The function y(t) = Pert-rt is a soln to s differential equation dy/dt = ry where P and r are…

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Q: Compute the divergence and curl of F= -(z³-3x)j+4y²k+x²yi

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Q: in a graph What is the cartesian product? And give an examples

A: Cartesian product is also called box product of graphs. The Cartesian product of 2 graphs, G and H,…

Q: Which of the following is not true? C 4dx 4dx A So √X(X+6) = lim So c+∞ ¹0 √x(x+6) 5 dx dx B S = lim…

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Q: Which of the following is ALWAYS TRUE about a function f? □ If f(x) is a rational function with…

A: Using definition of derivative

Q: (0.01)365 O True O false > (1.00) 365

A: Check the statement

Q: Given the function y = 2x³ - 4x² + 5, find its derivative.

A: Topic = Derivative

Q: use the graph of the function √²³ (x³²-6x) dx to explain the geometric meaning of the value of the…

A: Given function ∫03 (x3-6x) dx This below image is the graph of the function

Q: a) Use the Product Rule to find the derivative of the given function. b) Find the derivative by…

A: Given  problem:- a) Use the Product Rule to find the derivative of the given function. b) Find the…

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

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Q: 3. Sketch the graph of one function f(x) that has all of the following properties: a.) The domain of…

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Q: 2. On the wall of Mr. Piamonte's house, a 6 meter picture was hung so that its location is 5 meters…

A: 2.

Q: 8. Consider an object moving along a line with velocity v(t) = 6t2 - 12t with t measured in seconds…

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Q: The general solution to the second-order differential equation 5y" = 8y' is in the form y(x) =…

A: Given,5y''=8y'That is5y''-8y'=0

Q: 2 Let f(x) = 5x4 -/+8√x-3. a) Find f'(x). (b) Find an equation for the tangent line to the graph of…

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Q: f2₁ (4x + 5) dx

A: ∫-12 4x+5dx

Q: LO 5 100 160 500 √√25 O +1 O -1 O +1,-1 None of them

A: We can find the solution as below.

Q: Find lim [x csc(x)] as x approaches zero.

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Q: 3. Apply the three conditions of continuity to determine if the function f(x) = 2x²+5x+2 x²-x-12 is…

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Q: The graph of a function f is given below. According to the graph, the derivative of the function f…

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Q: (a) What angle in radians is subtended by an arc 1.50 m long on the circumference of a circle of…

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Q: 2. What details are used in order to analyze the polynomial function and analyze to sketch the…

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Q: > > f(x) = 2x * d F(x)=(√2x+2/2) f' X+ dx f(x) = , (Vzx) = dx 2√2 x لعلم قواعد العاه م حسب الم d |…

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