(d) +ỷ =0 dy dt (e) (f) d²y dt² d³y dt3 + sin(t + y) = sin t +t + (cos² t) y = t³ dy dt

Q: Consider the vector field F (x, y, z) = (z + y)i + (4z + x)j + (4y + x) k. a) Find a function f such…

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Q: f f(x) = x+5*. find the derivative of this function f'(x) A. f'(x) = 5* In 5 B. f'(x) = -1 + 5* In 5…

A: Here we have to find the derivative of the function.

Q: -1 Using Doolittles method for the following matrix A = 0 L-2 L- matrix and U - matrix. 2 11 86 0 51…

A: Given, A=-121086-205

Q: Write the interval of continuity for the function below: tan(cos(x)) log6 (7) f(x) = for 0x< 2π

A: The given function is: f(x)=tan(cos(x))log6xπ

Q: (1³7). (a) If Q is the point (x, sin(¹37)), find the slope of the secant line PQ (correct to four…

A: We have to find the values  of slope at given value of x.

Q: 30. dy dt t y-12y y(0) = 4

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: Find the area of the segment cut off from the curve y = sin x, 0≤x≤ n by the line y = 1/√2. H4 34 y…

A: Let's find area of segment.

Q: 5(4) + 3y(3) = 0

A: Let's solve given differential equation.

Q: B.    Find the DE of each of the following by eliminating arbitrary constants               1.…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: Toflow (2) y = √sinh √tan x

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Q: The equation y² = cx is the general solution of

A: We have to find the differential equation.

Q: For the following function models the position s(t) of an object moving along a stright line, where…

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Q: The point P(1, 0) lies on the curve y = sin( (a) If Q is the point (1) 2 = sin(13). CIEN : (x, sin(…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: A V(t) = -1,700t + 32,000; value after 5 years = $23,500

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Q: Q8. Let ABC be a triangle in the E.G. Assume E, F points on AB. AC respectively such that…

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Q: Graph and find the domain and range for y= sin²x + 1

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Q: Solve the differential equation, such that the equation passes through the given point (x, y).…

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Q: Use Horner's method to evaluate P(x)= x - 4x²-3x+5 at po = -2. b) Use Newton's method to find p₁.

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Q: 2+2x-1 dx x³-x

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Q: f(2cot 2x² - 2e²) dx

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Q: 1 3. f(t)=√3-2t; f(1), f(−3), ƒ(0)

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Q: → If I is a path-independent vector field, with 00 F. dr = 4.1 and ((11) F · ďr = 3.3 and (0) F · dr…

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Q: B. by factoring 1. x² + 7x = 0 2. m² + 8m = -16 3. x2 + 5x − 14 = 0 4. 2y2 +8y - 10=0

A: Topic = Quadratic equation As per guidelines , At a time only three sub-parts can be answered.…

Q: Find c such that the function x ≤ c { is continuous everywhere. f(x) = x² - 3 X 6x 12 x > c -

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Q: (cos-14x)2 √1-16x² 5) S (t) - dx

A: To find out the integration.

Q: 1. f(x) = x 3x-1

A: Domain of a function is defined as the values of x for which the function is defined.

Q: Prove that: В(х+у) тв (хун) = в сху) let П (х+1) =Х ГСХІ

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Q: A differential equation is an equation A that contains a derivative like y'(x) as well as the…

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Q: Solve the initial value problem. dy 3 dx - = x˚ (y - 5), y(0) = 9

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Q: Which statements are true about matrix A if a ‡ 0 and a² #b²? b b a A = a [8 There is a unique…

A: Please see the below picture for detailed solution.

Q: d'y 2) Find the dr for the function y = secx. Reminder: combine all similar terms.

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Q: Find dy/dx for the following functions:- u² (4) y=²+1 , u = 3x² - 2 (3) 4x² + 3xy - xy² = 0

A: We can find the answers in the below steps

Q: if f(x) = x²√√In x² P x A. f'(x) = . find the derivative of this function f'(x) 1-In x² x²√√In x²…

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Q: Change the following integral to polar coordinates and evaluate: 4-x² [2² 0 x² + y² dy dx Sketo

A: To convert Cartesian coordinates into polar coordinates we use the following transformation, x=rcosθ…

Q: J. (1+vx), √x dx

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Q: f sec (5x)tan (5x) dx A. 5 B. 1/2 cos 5x + C C. tan 5x + C D. 15 sec 5x + C ²5 csc 5x + C

A: The given indefinite integral is: ∫sec(5x)tan(5x)dx Necessary formula: ddx(sec x)=sec x tan x ⇒∫sec…

Q: A. by extracting square roots. 1. x2 = 169 4. (x - 2)² = 16

A: Answer (4) We have to solve by extracting square roots (x - 2)2  = 16

Q: Q6. Let O(0,0), A(1,0), B(1,4) be points in the plane R². Then the following point lies in the…

A: I am attaching image so that you understand each and every step.

Q: (2cot 2x² - 2e²) dx A. 1/cot 2x³ + 2e²+ C 2

A: To find out the integration of the given function.

Q: List the x values of the discontinuities of the function: 4 1+ e4/r y = X =

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Q: A. by extracting square roots. 1. x2 = 169 2. 9b2 = 25 3. (3y - 1)2 = 0

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Q: Topic: Differential Equations/Homogeneous equations Please find the particular solution of y2dx+x(…

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Q: 41. How close to -3 do we have to take x so that 1 (x + 3)4 > 10,000

A: See this solution in below.

Q: 4. Find the surface area when the function y= 6 + 1 2x on the interval 1≤x≤2.

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Q: xdx e-x + (Y+) dy уз = 0

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Q: √ ¹ (1+√x)3 √x - dx

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Q: You borrowed money and need to pay interest on the loan. You must pay 5% of the $6700 loan to remain…

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Q: A graphing calculator is recommended! If a ball is thrown into the air with an initial velocity of…

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Q: Express the repeating decimal as a fraction. 4.717171...

A: Given,            4.717171....To find : Express the repeating decimal as a fraction.