Find the DE of each of the following by eliminating arbitrary constants. Reduce your final answer in simplest      2. y= C1x + C2e-4x  ( Hint: multiply by e4x)

Q: Find the arclength of the curve r(t) (6 sin t, 2t, 6 cost), -2 < t <2

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Q: Prob 2 Use the Direct substitution rule and justify why you can use it to evaluate Лет 2-2 ln x + ex…

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Q: Find the area of the segment cut off from the curve y = sinx, 0≤x≤nt by the line y = 1/√2. HT 1/2 y…

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Q: 1. Find the DE of all straight lines with slope and y-intercept equal.

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Q: Add. 7 9 2 (x+8)² x²+x-56 + 7 9 2 (x+8)² x²+x-56 (Simplify your answer.) +

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Q: Calculate 127 y [1/10 ds where C is the parabola r(t) = (t, t², 0). Let 1 ≤ t ≤ 4. X

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Q: Solve the Differential Equations. 3.44 Test for homogeneity 3. f(x, y) tanx - sec²x - cosy

A: Let's find function is homogeneous or not.

Q: 4. Find the second derivative of Y with respect to x for 4x² + 8y² = 36

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Q: Find the differential equations for each family of curves under the following conditions: a)…

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Q: Find any relative extrema of the function. (Round your answers to three decimal places. f(x)=…

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Q: 3. Check that each given function is the solution to the initial value problem. y(0) = 1, y'(0) = 2,…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: A circle has the equation 4x² + 16x + 4y² = (a) Find the center (h,k) and radius r of the circle.…

A: Given Equation:- 4x2+16x+4y2=0

Q: Q4: Solve the following integrals:- dx ³-2x² (1) dx (2) √ √2√9-1² (3) fx² sinxdx (cos-14x)² 1-16x²…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

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: 2) Consider the function defined by g(x) = 5x - 4. You may use the graph of this function to…

A: Recall: Derivative(|x|)=xx

Q: A company produces a special new type of TV. The company has fixed costs of $497,000, and it costs…

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Q: The following questions should be completed and your answers brought to class. Spending on Baseball…

A: Given graph: The given graph is a bar graph. In bar graph, height or length of the bars are…

Q: Find the equation of a line that passes through (-1,-3) and is perpendicular to y=-4x+2

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Q: y = Clx+ C2e

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Q: Find the indicated composite function 6. f(x + 1) where f(x) = x² + 5

A: To find the f(x+a) when f(x) is given then we just replace x of f(x+a),  where a is an integer.

Q: Find the x-values (if any) at which f is not continuous. If there are discontinuities, determine…

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Q: 3) f(x) = x--x- 1; [3] [1, -1: 01.4 5) f(x) = 2x² - 2x -1; 4) f(x) = −x- - x + 1; [2, 1 x-1 6)…

A: Average rate of fx change over interval a,b=fb-fab-a

Q: Question Define as the region bounded by the functions u(y) = 2 and v(y) around the y-axis, what is…

A: Here we have to find the volume of a region when revolved about y axis.

Q: Using continuity, evaluate the limit: - 1 sin(z + sin(x)) lim X→ -

A: Topic- Limits

Q: 3) Consider the function defined piece-wise as follows: f(x) = 4x + 1 for x < 0 and f(x) = (4x - 1)2…

A: The function piecewise defined as follows: fx=4x+1for x&lt;0(4x-1)2for x≥0

Q: 2. dx tanx 4t² dt

A: To differentiate the given function.

Q: Let if x < 1 f(x) = {(x - 2)² [x² + 1 [(x - 2)² if x = 1 (a) Find limx→- f(x) and limx→+ f(x). (b)…

A: Given: For (a), limx→ 1-x2+1Plug in the value x=1=12+1=2limx→ 1+x-22Plug in the value x=1=1-22=1

Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

A: Solution: Given, Circle having center at (0, 0) and radius is 5 and

Q: I 3 r 2 T 3.Evaluate 2 [2 sin x] dx = , where [] is define the greatest integer function.

A: Integral

Q: Find the scalar and vector projections of b onto a. a = (4,7,-4) b =(4,-1, 1)

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Q: 1. Use the tables to find the z transforms of the following a. 6 b. 2 c. e 2n

A: As we know that, L{1} = zz-1

Q: A. Solve the given problems: Show your solution. 1. Use Richardson Extrapolation to estimate the…

A: Given function, f(x)=cos(x), x=π4, h=π3 to h=π6

Q: List the x-values where the function is not continuous: f(x) = -x+ 3 if ex if if 3 – x x < - 3…

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Q: Prove that: B(x+1; y ) + B (x,y+1)= B(x,y) let (x + 1) = X(X)

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Q: D. using quadratic formula. 1. x2 + 5x = 14 2. 2x² +8x - 10= 0 3. 2x² + 3x = 27

A: Topic = Quadratic equations

Q: y = cof'/ x2-1 x²+

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Q: Q2/Solve the following equation from t=0 to 1 with step size is 0.5 using E Method. dy -= y sin³ (t)…

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Q: day 2x + 5x dx4 dy 3 dx' - xy = 0

A: To write down the degree and order of the differential equation.

Q: Prove or disprove the following: For any integer x, if x + 5 is even, then x + 1 is even.

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Q: f(t) = 2 2 (3 cos 6t-5 sin 6t)

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Q: (3) fx² sin x dx (4) S (cos-14x)2 √1-16x² -dx

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: Simplify the expression by first getting common denominator, then pulling out any common factors in…

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Q: Write the sum using sigma notation: 7 + 10 + 13 + 16 + ... + 40 = Σ B, where n=1 A = B=

A: As per our guideline we can solve only first question you can repost other question in next question

Q: The demand for a new computer game can be modeled by p(x) = 46.5-6 In x, for 0≤x≤ 800, where p(x) is…

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Q: Find the arclength of the curve r(t) = (9√√/2t, et, e-9t), 0 ≤ t ≤ 1

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Q: The solid S has a base described by the circle x² + y² = 1. Cross sections perpendicular to the…

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Q: 2. Find (a) I (b) dy dx y = coth(lnx) y=xtanh’(VF)

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Q: 1. fx² sec x³ tan x³ dx

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: So 1 x²+7x+10 A. B. C. D. 3ln 2-ln 2 3 3ln 2+ln 2 3 3ln 2-ln 2 5 3ln 3-ln 2 3 dx

A: The given integral, ∫011x2+7x+10dx use the integral formula, ∫dxx=ln x+C

Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): x² 4 x -2 f(x) = { mx² 2 m = n =…

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