Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the interval [1,2].

Q: Fill in the blanks the information needed to make the solutions correct.

A: 1)∫23(t3+5) dt2)∫12(x2-x) dx

Q: Draw a picture to find ALL angles in 0 ≤ 0 < 2TT. 1 Ay mple: For tan(0) = = draw a circle. Label the…

A: Topic :-  trigonometry

Q: Q4:Evaluate 1) lim (1-²) x-0 \sin x

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Q: TICILNIC B. Find the general solution of the following 2nd order differential equation: y* +2y + 2y…

A: Topic:- differential equations

Q: 9.f tan3³ x √sec x dx

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Q: 1.) lim f(x) = X→-7+ 3.) f(3) = 5.) f(0) = 7.) lim f(x) = x→0+ 9.) lim f(x) = X→3+ 2.) lim f(x) =…

A: The objective is to determine the limit if it exist.

Q: (b) Find the points on the given curve where the tangent line is horizontal or vertical. r = 1 + cos…

A: We are given a curve in its polar form  r= 1+cosθ We have to find points on the curve at which…

Q: (a) Find the slope of the tangent line to the given polar curve at the point specified by the value…

A: We have to find the slope of the given polar curve at the point specified.

Q: 3. 4. If =(-12, 4, 8) the position vector of u is.............

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Q: y = ln √4x² (Hint: Apply first a property of LOG.)

A: Let's find first derivative.

Q: 6. (10 points) Give the equation of the tangent line of the following function at point a = 1: xe…

A: Solve by Differentiation

Q: 5. y = 5 tan x³ + sec (3x)

A: Topic = Derivative

Q: 4. 2x3ý = y (y² + 3x²)

A: The given differential equation is  2x3y'=y(y2+3x2).

Q: Question 19 Given f(x,y) = ex cos y, Evaluate fx(0,2) A) e² B 0 (C) -sin 2 D) cos 2

A: Topic = Derivative

Q: Question E.) 36 Al 2+3^ 3^ +4^

A: Explained below

Q: Question 38 What integration technique can be used to integrate: (A) Power Formula Integration By…

A: Here we have to determine the integration technique to solve the given integration. =∫5dx3+x2

Q: Solve the given ODE using the method of undetermined coefficients. y" – 4y = (x² − 3)(sin2x)

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Q: Consider the function f(x) exact values. f'(x) = f''(x) = f'''(x) = = Compute each of the following.…

A: Topic:- derivatives

Q: : Evaluate the following integrate: 1- S x²dx √√9-x² 2-[(2 + 5x)e³ dx

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Q: a. Solve 2 cos(2x) = √2 for x

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Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A: Topic = Derivative

Q: Given Cost and Revenue functions C(q) =q³-8q² +54q+5000 and R(q) = -3q² + The costs are $ (Round to…

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Q: Simplify to an expression involving a single trigonometric function. Please show work so i can…

A: SOLUTION-

Q: 5 8. fcscz x cot3 x dx

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Q: What is the particular I solution of the differential equation (2x + y²) dx + 2xydy = 0 when x = 1…

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Q: 9. A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 4√108…

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Q: dy Q1: Find the for the following functions: dx 1- y = e(x+ln 5x) 2- y cosh-¹ sin 2x -1 3- y = asinh…

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Q: Given f(x,y) = x²y-3xy³. Evaluate (A) 2x²-12x B (C) (D) -6y3+8y/3 14y-27y3 6 6x² - 45x 4 2 1 fdx

A: Topic = Integration

Q: A bicycle with 24-inch diameter wheels is traveling at 16 mi/h. Find the angular speed of…

A: A bicycle with 24-inch diameter wheels is traveling at 16 mi/h.

Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: (D² - 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

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Q: Using integrals, find the area bounded by the following:  f(x) = 4x2 + 20 g(x) = 8x + 32 x = - 4…

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Q: 2. Let S be the part of the cone z = √² + y² that lies between z = 1 and z = 3 with upward pointing…

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Q: A landowner wishes to use 2 miles of fencing to enclose a rectangular region of maximum area. 1.…

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Q: 2 Find all local extreme values of f(x) = -2.3 + 11x² 56x + 30. 3 The FIRST local extreme value,…

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Q: 01: A. Find the general solution of the following Initial Value Problem (IVP): y+9y-10y = -40t²-72t…

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Q: Find the transition points. y = 15x³ + 360x² (Use symbolic notation and fractions where needed. Give…

A: Thr solution is given in the next steps.

Q: Find y" 13. y = x²sin (3x)

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Q: f(4)(x) an f(³)(x) = √√√x, f(4) (x) 6 7(6√x) X

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Q: Find the transition points. y = 3x² - 42x6 (Use symbolic notation and fractions where needed. Give…

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Q: 03: Fill in the blanks in the following: 1. If a (3,-2, 6) and b=(4,-1,-6) the axb = ******** .

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Q: If g'(6) = 6 and h'(6) = 19, find f'(6) for f(x) = f'(6)= (Simplify your answer.) () = g(x) + =…

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Q: (b) Find the area of the region that lies inside the first curve and outside the second curve. r = 1…

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Q: 1 2 3 4 5 ements below that you agree with. be checking more than one box. No partial credit.…

A: Topic:- calculus

Q: y = log₂ (1+x²)

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Q: Find x and y such that 64, x, y, 1 is part of an x = , y = Then find x and y so that the sequence is…

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Q: 4. y = = csc 1+2x) cot(1-2x)

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Q: Find the antiderivative F(x) of f(x) = 8(sec x)(sec x – 4 tan x).

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Q: Write an equation of the tangent line to the curve f(x) = answer in the form Ar+By+C =0. 3x at the…

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