f(x) = Answer: 1-cos(4x) 1+cos(4x) 2 sec² (2x)

Q: Find the solution of the IVP: (1 + y cos x) dx - sin x dy = 0, y(1/2) = 1. Then, evaluate y(1.603).

A: This question can be solved using the concept of linear differential equation.

Q: Consider f(x)=5x-3-41/x^2 Which of the following does the x-intercept of the tangent line at x=2…

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Q: 21-22 (a) What are the domain and range of f? (b) What is the x-intercept of the graph of f? (c)…

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Q: 3. Check for homogeneity and obtain the general solution. (Let 4C=C) (x² + y²)dx + xy dy = 0

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Q: 56x²5x-50 15x²-44x-20 20x²7x-6 2x² + 9x + 10

A: We know that the root of quadratic equation ax^2 + bx + c = 0 is x = ( -b + √ (b^2 - 4ac)) / (2a)…

Q: x Find z. if z = xvey.x = rcos(t), v = rsin(t), when r = 2 and t =

A: Given; z=xyex/y, x=rcos(t), y=rsin(t)

Q: Solved the following set of equations 16x + 2y 2z = 16 2x 14y + 4z = -8 4x + 2y + 18z = 24 Using…

A: The solution is given by below steps

Q: 1. A carpenter can construct book cases at a cost of P400 each. If the carpenter sells the book…

A: Given:- Carpenter sells the book cases for x pesos each And 300-2x book cases will be sold per month…

Q: Minimize the function M=3x² + 3y² subject to 2x+y=64 and find the values of x and y at which M is…

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Q: Solve y = (1 + y) sec (x) + tan (x)

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Q: = (1) cotr 1+csc.x

A: We will find the required.

Q: -9y+7z = 5 -11x + 17z = -4 13x + 18y = 4

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Q: Rewrite each of the following as a power function in the form kx", or state that it is not a power…

A: Given, 5x3;x3;72x

Q: Use integration to find the general solution to the differential equation: a) x² + y² + x + 2y = C…

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Q: lim ex-4 X→4

A: Using tabular methods to calculate the limit at x tending to 4.

Q: Evaluate the limit: lim x-6 x² + x - 30 x + 6

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Q: 2. If x = t + cost, y = sint, find d²y dx²*

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Q: Find (f 1)' (a) f(x)=3x³+4x²+6×+5₁ a=5 f(x) = x³ +3 sinx + 2 cosx, q=2 f(x) = 3+x² + ton (₂),…

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Q: then n = √a· √² = √d" 5 n q q and m =

A: am.an = am+n .

Q: Use PMT= 3¬ to determine the regular payment amount, rounded to the nearest dollar. The price of…

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Q: 5. Choose the correct answer for the number of (a) the vertical asymptote(s) (b) the horizontal…

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Q: Determine the solution of the 1st Ordered Differential Equa 3(x² + y²)dx + x(x² + 3y² + 6y)dy = when…

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Q: EXAMPLES Find an equation of the tangent line to the parabola y--&x+9 at the point (2.-3). SOLUTION…

A: Find equation of tangent line

Q: cm 10 cm

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Q: lim x118 x³ + 8x 2x³ + 5x² - 2x - 2

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Q: Find the difference quotient (z+h)-f(z) for the function given below. f(x) 1²+1+2 Give a simplified…

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Q: Question 1: Let f be a function and let h be a non-zero real number. Then the derivative (when it…

A: We have to tell true or false Answer (1)

Q: 8 x²+2 2 √x dx

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Q: 4 f(x)=x+acos x, where a is a positive constant and 0≤x≤ 2. Find the x-coordinates of all points,…

A: The function is given by fx = x+acos(x), a>0 and0≤x≤2π The equation of the line is y = x+a To…

Q: Let f(x)= -6 cos x + 6 tan x Find ‘(x) Find ‘(π/3) My results were the following: f’(x)=…

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Q: Finding the critical point(s) of f(x) on the given internal. f(x)=(2^x)sin(x) on [-2,6]

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Q: integral

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Q: Consider the equation below. x² + y² - 2x - 8y - z + 17 = 0 Reduce the equation to one of the…

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Q: Find the slope of the tangent to the curve y = 3 + 4x2 - 2x3 at the point where x=a .

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Q: Use the step-by-step or Euler method to solve numerically each of the following. (b) dy/dx = x+v,…

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Q: III. WITHOUT SOLVING the given problem, DEFINE the variables and unknown quantities, and SET-UP ONLY…

A: We have given a vacation house is rented.  Let,  x represents numbers of days C(x) represents cost…

Q: Find the relative extreme points of the function, if they exist. Then sketch a graph of the…

A: The given function is  f(x)= x3-12x+7  We have to find  a) relative minimum points b) relative…

Q: QUESTION 1 Determine the solution of the 1st Ordered Differential Equation: xy³ dx + ye dy = e-*dy

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Q: Given s(t) = 3t² + 3t, where s(t) is in feet and t is in seconds, find each of the following. a)…

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Q: Evaluate the integral. *π/4 [" sin ³(x) dx

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Q: Use the tabular method and the properties of limit to find the limit 1) lim 2 X-0 х (²)

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Q: X-2 (a) lim x2-7x+10

A: as per the company rule we are supposed to answer only the first question and rest can be reposted.

Q: Differentiate the following function. f(x) = x5 e5x f'(x) =

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Q: When a Rational Function has been simplified and graphed, it shows: 3 Vertical Asymptotes, 2 Points…

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Q: Find an equation of the tangent line to the graph of y = B(x) at x = 6 if B(6) = 0 and B'(6) = -1/2

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Q: 7. (x−y)(4x + y)dx + x(5x - y)dy = 0

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Q: Differentiate the function. y = (5x-4) (3-x3) 3 dy dx

A: Given :                    y=(5x-4)³(3-x³)³ Here, it is in the form of product of two functions.…

Q: Consider f(x) = 5x-3 - 41/x^2 c) Find the equation of the tangent line at x = 2 to the graph of y =…

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Q: MATH 12 Worksheet 2: Fundamental Theorem of Calculus 1. Definite Integrals and the Fundamental…

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Q: Consider the following graph of y = f(x): s What is the lim fx f(x) x-0 A.0 B. 1 OC. -1 D. 2 E. The…

A: From the graph we can see that as x tends to 0, f(x) tends to 1.