3x 1. S dx 1+3x

Q: 2/ Find the value of the limit: lim x/*,

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Q: d d Calculate r1(t)· r2(t)] and ri(t) × r2(t)] first by differentiating dt dt the product directly…

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Q: Find the arc length L of the graph of r(t). r(t)= 4 cos(t)i + 4 sin(t)j + tk, 0 ≤ t ≤ 2π

A: The formula for the arc length is given by: L=∫02π(x'(t))2+(y'(t))2dt Here,…

Q: Use De Moivre's theorem to solve for z given z = 3 – 2i. Write your answers in rectangular form. Use…

A: Given: z5 = 3-2iz   = 3-2i15                                     1-------------------De-Moivre's…

Q: x In x dx

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Q: ||r(t) × r"(t)|| ||r"(t)||³ Use the formula k(t) = to find k(t). r(t) = eti+ej

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Q: 1 Suppose that L is a location function of an object, given as L(t) : We 2t – 3 will compute the…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Given that 5i is a zero of p, write the polynomial in factored form as a product of linear factors:…

A: Given that the polynomial is a6-11a5+65a4-331a3+1024a2-1400a+600 and 5i is a zero of the polynomial.…

Q: Using a method of reduction to separable equation and reduction to linear equation, find the general…

A: Let's find.

Q: Find an equation of the tangent line to the graph of y = x^3 − 1 at the point where x = 2.

A: To find the equation of the tangent line at x=2.

Q: a1, a2, a3, . be a geometric seq is also a geometric sequence by that af, a3, až, (a) Σ (1- ). (Φ)…

A: topic - sequence and series

Q: Given below is the augmented matrix of a system of linear equations.

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Q: Activity 1.4.3. For each of the listed functions, determine a formula for the derivative function.…

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Q: Differentiate the function. g(u) = 7u + V 5u

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) x(2x + 5)8dx

A: Explained below

Q: 3. a) If 2 - i is a root of x³ – 2x² – 3x + 10 = 0, find the other complex root. b) Calculate the…

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Q: Convert the point from cylindrical coordinates to spherical coordinates. (6, 7, 8) (р, в, ф) -

A: Given: Now, we need to convert the point from cylindrical coordinates to spherical coordinates. We…

Q: Estimate cos E- 0.1) + cos

A: Follow the procedure given below.

Q: Question 7 Find the area enclosed by the curves y=2r², y=2x.x=- and x = 1 A) 45/51 B 65/89 59/76 D)…

A: Here is the solution

Q: Write an equation for the function graphed below. Use the smallest powers possible to meet the…

A: To find the equation of given graph.

Q: A woman standing on a cliff is watching a motor boat through a telescope as the boat approaches the…

A: Let x be the acute angle made by the telescope with the vertical.

Q: Q11. Suppose z = f(x, y), x = g(t), and y = h(t) satisfy: h(7) = -2 h'(7) = 1 f-(2, –2) = 2 fy(2,…

A: Suppose z=fx, y, x=gt, and y=ht satisfy: g7=2, h7=-2, fx2, -2=2g'7=-3, h'7=1, fy2, -2=0By using the…

Q: Evaluate the limit, using L'HÔpital's Rule if necessary. sin 3x 1. lim x→0 tan 8x In x5 2. lim x7 –…

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Q: B) Find for the Implicit function: dx x? – sin(xy) + y? = 5xy

A: The given equation is; x2-sin(xy)+y2=5xy.

Q: Find the average value gave of the function g on the given interval. g(x) = 3x, [8, 64] gave =…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: z = 0, y = 1, у %3D1, z = x² + y? y = x².

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Q: Let f(1) = 5I + 2. Using the definition of derivative at a point, %3D a. enter the expression needed…

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Q: If B = exp(r - 2), what is VxB?

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Q: 10 9. Consider the function f(x) %3D Let F(r) be the antiderivative of f(z) with F(1) 0. Then F(x)

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Q: 4 sin (In t) cos`(1nt) dt 5.

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Q: 7- Use the limit definition to compute f' (x) and find equation of the tangent line at r = 3. f (z)…

A: topic - derivative of a function using limits

Q: 9- If a person with O'Micron virus coughs, It will spread the virus in a spherical form, determine…

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Q: dy 5. Solve the differential equation = 7xy3 if y = 0.5 when x = 2. dx

A: Given query is to find the solution of the differential equation.

Q: Find the area of the region under the graph of f on [a, b]. f(x) = x2 - 8x + 20; [-1, 2]

A: The detailed solution is given below Thank you

Q: 75 then compute the limit. 137 2| %3D Investigate the one sided limits (left and right) of f () =…

A: Given query is to find the limit.

Q: Find Inz3 dz

A: LetI=∫lnz3zdzLet z3=udifferentiate 3z2dz=duDivide 3z2 on both sidedz=du3z2dz=du3z2Divide z oboth…

Q: A line passes thru (3, 4) and cuts a right triangle with the coordinate axes in the second quadrant…

A: Suppose the line is: xa+yb=1 where a and b are the x and y intercepts respectively. Now, it passes…

Q: Given the function g(x) = 6x° + 72r² + 270z, find the first derivative, g' (1). gʻ(x) = Notice that…

A: g'x = derivative of gx with respect to x g''x = derivative of g'x with respect to x if at  point…

Q: 3. a) If 2 - i is a root of x3 – 2x² – 3x + 10 = 0, find the other complex root. b) Calculate the…

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Q: Find the cost function for the given marginal cost and fixed cost. See Example 8. Marginal Cost…

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Q: 7. S(x – 9)7 dx 8. S: r5 dr V3-r6

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Q: d²y 2. Find the second derivative, dx2 a. x = t2 + 1 and y = t3 t2 + 2 and y = sin(t + 1) b. x = | 2

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Q: 12. Find the flux of the field F(x, y, z) = 4xi + 4yj + 2k outward (away from z-axis) through the…

A: Flux of the given field is given by

Q: 15. S(x + 2)²dx

A: Solve the following

Q: Prove that lim 1 1 by definition.

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Q: Evaluate the indefinite integral. x2 dx 0.2x3 + 2.7 + 2.7

A: topic - indefinite integral

Q: Q2) Solve the D.E xdy + (2y-x+ 3x)dx 0

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Q: 12. L(s? – 1) sds 13. (1² – #) dt

A: ∫xndx=xn+1n+1+C , C is a constant for any real number n.