Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the function f is differentiable at the point x-2? why?

Q: The graph shown is f(x) = √√x + 2. 2 + X 54-3-2-1 1 2 3 4 5 -2- 3 What is the integral function that…

A: Using vertical strip

Q: Binh Xi 5X₁ L 0X₂ zj-cj o b C a X3 Si 2 1 -8 -1 7 S₂ 0 1 SoL 30 10

A: Apply simplex method

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

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Q: the tangent plane of the surface [ z=x^5+e^(xy)cosyx] at the point (1,0) O z=5x-y-3 O z=5x+y-3 O…

A: Above question is solved.

Q: In x -2 x dx

A: Given: I=∫12lnxx2dx   Apply the integration by parts to solve the given integral. ∫udv=u·v-∫vdu

Q: Find the area of the triangle below. Carry your intermediate computations to at least four decimal…

A: Given.

Q: Find the equation of the plane that passes through the points (3, -2, 2), (-9, 2, 4) and (-6, -4,…

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

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Q: The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial…

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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: Solve the following integrals. 3.) S fafy dxdy y²-x²

A: On solving this we will get

Q: Calculate the arc length of y = 9x + 1 as x varies from 0 to 5. S -

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Q: Solve the differential equation by the method that you think is most convenient.   (y + √(xy)) dx -…

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Q: Determine the cardinality of each of the following sets. a. A x B, where A = {a, b, c, d, e}, B…

A: a) A=a,b,c,d,e, B=xb) a,b,cc) d) Φ,Φ,Φ,a,

Q: = C₁e^ + c₂e^, (-∞0, ∞0); y" - y = 0, y(0) = 0, y'(0) = 5 ex- 25e-x X

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Q: Solve the given differential equation by using separable variables. 1. dy x-5 = dx y²

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Q: Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x)…

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Q: Find a power series representation for the function. f(x) = x2 tan-1(x3) f(x) = Σ n = 0 Determine…

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Q: exact method: (3xy3 + 4y)dx + (3x2y2 + 2x)dy = 0

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Q: COS X 1+ sin² x dx

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Q: Sketch the graph of an example of a function that satisfies all of the given conditions limx)=0 lm…

A: TO FIND: Correct Graph of the function

Q: 49 - x² Evaluate the integral: dx 8x² (A) Which trig substitution is correct for this integral? x =…

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Q: √tanx secox dx

A: Given problem:- ∫√(tanx) sec6x dx

Q: For the function below, find a) the critical numbers; b) the open intervals where the function is…

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Q: Let f(x)=x²+2x if x<5 - Cx if x 25. For what value of the constant c is the function f continuous on…

A: We have to calculate the value of c

Q: 10-13. Limit definition of the definite integral Use the limit defini- tion of the definite integral…

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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: Approximate using differential √627( answer in fractional form)

A: Let y=f(x)=x4where x=625 &amp; ∆x=2

Q: Find a plane through the points (3,4,-1), (-6,-7,-1), (8,1,6)

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Q: Find the slope of the normal line to curve x=4sint, y=cos2t when t=

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Q: Find the derivative of the following functions by using the limit definition of the derivative.…

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Q: Is it possible to get the area 2 3 between y² = 3x and y = x³, using a. vertical strips b.…

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Q: There are 3 red, 4 green, 4 white, and 5 blue marbles in a bag. If you select 2 marbles, what is the…

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Q: 182 Σί What is the value of the expression 1?

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Q: y = 1 x=y² B A (0,0) y=x² C (1, 1) X=1 X

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Q: Determine whether the given function is even, or odd, or neither. One period is defined for the…

A: We have to find if the function is even or odd.

Q: -TL 4.) x² sin(xy) dydx

A: Given ∫0π∫01x2sinxydydx

Q: Find an antiderivative F(x) of the function f(x) = 5 sin(x) such that F F(7) 2 F(x): Now, find a…

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Q: Evaluate the following 3 3 x4 + 2x³ + 3 X² + x + 1 x4+x² 2

A: We have to evaluate the integral.

Q: Evaluate the double integral: S² SATI 1/3 x² +1 (Hint: Change the order of integration to dy dr.) dr…

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Q: Solve step by step the following problem (be clear please) XXXXXXXXX Calculate the roots of the…

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Q: find the solution of the problem with given initial value, using homogeneous equations with constant…

A: Here we have to the differential equation.

Q: 5. csc 6x dx

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Q: Use false position method find the diameter (D) of the pipe which satisfies the follow ation:…

A: answer is in next step

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.

Q: The amount of carbon 14 present after t years is given by the exponential equation A(t)=A0ekt​,…

A: Here, given that the amount of carbon 14 present after t years is given by the exponential equation:…

Q: (B) let y = 3sin5x - 2cos5x show that ax y + 25y = 0

A: Given :y=3sin5x-2cos5x

Q: Use the angle in the unit circle to find the value of the three trigonometric functions below. 1 2…

A: Topic = Trigonometry

Q: the normal line of the surface [z = (4x^2 + y^2] at the point (1,1,5) O 8x-2y+z=5 O 8x+2y+z=5…

A: We have to find the normal line of the surface.

Q: S. (2w² - 5w+3) dw 4. S. (36+4) ² db 1 v dv S. 6. v² 7. J. ze³z²-1 dz 8. S.2²2 ydy 5. e

A: