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Q: Differentiate the function. R(a) = (6a + 1)² R'(a) = 12 X

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Q: 5. Find the particular solution to the differential equation y√1−x² y' − x√√1—y² = = 0 given the…

A: we will use substitution method to solve this differential equation

Q: 7. Use the definition of the limit of a function to show that if lim f(x) = a and lim g(x) = b, x→x0…

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Q: Find f[g(x)] and g[f(x)]. f(x)=√x+3, g(x) = 12x² - 7 f[g(x)] = g[f(x)] =

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Q: Please show all work. Please solve by parts for the following DE. x^2y'-2xy=1 , y(1)=2

A: Given that , x2y'-2xy=1 , y1=2 Find the solution of DE.

Q: Quadrant I Quadrant II 33π 4 7T 11 13п 3 5T Quadrant III 7T Eco 13п 9 Quadrant IV

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Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

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Q: Let f(x)=3e^x+4+e^−4 f′(0)=

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Q: Differentiate the following function. y=ets dy dx = d dx )= lets

A: To find the derivative of the given function.

Q: 3. (2 + ln x)³ √ (2+1) X A. (2 + ln x) 4 +C -dx C. (2 + Inx)³ + C 4 {1tinx? Syn (2+1mx) +C 20 B. (2…

A: We can solve the integral using substitution method. Here we substitute 2+lnx by z and then apply…

Q: Let z(x, y) = -7x² ++ 3y² where x = s + 9t & y = -98 + 6t. = Calculate Oz əs Oz Ət дz ds and Oz Ət…

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Q: n { ( ₁ + ² )"} n (f) {n(√n² +1− n)} (e)

A: Sequence is convergent if limit of the sequence exists finitely.

Q: Find the length of the curve. r(t) = (5t, 3 cos(t), 3 sin(t)), -9 ≤t≤9 Step 1 For r(t) = (f(t),…

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Q: Use the graph of the function below to find: a) Coordinates of its vertex (h,k)¸ b) Intercepts. c)…

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Q: If f(x)=x³√x), then ƒ (4) (16) =

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Find an equation in rectangular coordinates for the surface represented by the spherical equation. π…

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Q: Solve the following for x. Give an exact answer using the log function. 7. (94x-6) = 77 X =

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Q: 1. Determine the derivatives using shortcuts of each of the following functions. Do NOT simplify a.…

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. 4x²+x+27 [ x3 +9x 3)…

A: Given integral:- ∫4x2+x+27x3+9xdx

Q: Find the point(s) on the graph of f where the tangent line is horizontal. f(x) = X x² + 25

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Q: A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

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Q: 39. Evaluate L{e²¹ cos 6t} (A) (B) S- -2 s² - 4s + 40 S- - 2 s² - 4s-32 40. Evaluate L-1 (A) cos 712…

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Q: Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = ti…

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Q: The terminal ray of angle B, drawn in standard position, passes through the point (-4, 3√/5). What…

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Q: f(x,y) = arctan(2x-3y)+ Find the domain and sketch it. In(x^2 +2x+y^2).

A: To find the domain of the function f(x, y), we need to consider the values of x and y that make the…

Q: Describe each line. a) [x, y] = [2, -5] + t[0, 1] b) [x, y] = [3, 7] + [2, 0] c) [x, y, z] = [-1, 3,…

A: Solution below

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Use the integral test to investigate the relationship between the value of p and the convergence of…

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Q: the value of the rac condition. Working Example 3: Solve an Equation With T Solve the radical…

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Q: Evaluate the following functions: (y-1)(y²+2y-3) y²-2y+1 a. b. 2 x-3x-4 x+1

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Q: Solve for x. log₂ (x − 28) = 3 X = (Separate answers by a comma.) If the answer is radical use…

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Q: Let a = (6, 3, 2) and b = (4, 6, 6).

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Q: (d) Passing through the point (0, 1, 2), perpendicular to the line L and intersects L. L(xo. v) =…

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Q: N .3 44. lim N→∞ 1N

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Q: nd the distance between the points. Give an exact answer and an approximation to three cimal places.…

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Q: please integrate using trigo substitution: ∫x/sqrt(3-2x-x^2)dx please provide complete solution

A: Given that a integration and we solve this integration by using general property of integral.   We…

Q: 2. Find 02z дхду for z = x2 tan-1 Y X

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Q: Find the derivative of P=155e^0.18t

A: p=155e0.18td dt(et)=et

Q: Identify the equation as separable, linear, exact, or having Integrating factor that is a function…

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: Two airplanes are flying in the air at the same height. Airplane A is flying east at 400mi/h and…

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Q: Find an equation for the tangent plane to the surface z + 4 = xy cos(z) at the point (4, 1, 0).…

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Q: Let -2x² - xy +10y² − 15x + 12y — 22 = 0. dy dx Use partial derivatives to calculate at the point…

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Q: (d) f(x) = log3 (6x − 1) - ln(6x - 1) + 4eª − e¹x - 1 a logb

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Q: Integrate TT y 2 x² dy dx.

A: To integrate ∫13∫24yx2 dy dx.

Q: A) f(x) = = = - 5x -5x [-3,3]

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Q: 44. Find the general solution of the DE (2y-x²) dx + (y + 2x) dx = 0. A. 2xy- 2xy-3-2²=C C. 2xy +…

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Q: Find the velocity, acceleration, and speed of a particle with the given position function. r(t) = 9…

A: Given: r(t) = 9 cos(t) i + 8 sin(t)j

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

A: Given;  r(t)=sqrt(2)ti +etj +e-tk.

Q: 9. Which of the following equations is (are) Bernoulli? dy (A) y + ln y = tan²(x + 5) dx (1+y)y =…

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Q: 28. Find a linear differential operator (of lowest order) that annihilates the given functio f(x) =…

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