Evaluate the definite integral. 2 St³√₁+t² dt 0

Q: Solve the initial-value problem 1. (D² + 4) v = 12; y(0) = 0 (0) = 2

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Q: 3. Find the exact value of surface area of the solid that is described by the intersection of the…

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Q: Express the number 5√3-3i in the form R(cos(0) + i sin(0)) = Rei, where R> 0 and T ≤ 0 ≤ π. NOTE:…

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Q: An exponential function f(x) = ab passes through the points (0, 7000) and (2, 4480). What are the…

A: The objective is to find a and b.

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

Q: 7. Use the Mean Value Theorem and find all points 0 <c<2 such that f (2)-f(0) = f'(c)(2 - 0). f(x) =…

A: topic:- function

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Q: Determine the equation of the parabola whose graph is given below. Write your answer in General…

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Q: (3) (3) (4) h. y = sin(x² + 1) i. y = 3e4x5 j. y = In√5x3+4

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Q: Evaluate 6252 6251 6250 6254 6253 Ads, where C is the right half of the circle x² + y² = 25.

A: To evaluate the given integral.

Q: What is the integral that represents the length of the curve from x = 2 to x = 4. Select one: 0 ₂²…

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Q: K O O Given the integrals I, J, K and L, where 3 dx = 6²° 3 .00 dx x + 2' O 1 = = [₁*√x- √x-3 dx, L…

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Q: The graph below shows a transformation of y S 5 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 y = 1 D 3 4 5 2.…

A: topic- equation of a function

Q: find the volume of the solid bounded by y=2x+1,y=3and x=4 about using the line y=10 the cylindrical…

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Q: Question 9 of 20 K View Policies Current Attempt in Progress Find the discontinuities, if any. f(x)…

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Q: The marginal cost of printing a poster when x posters have been printed is dollars. Find c(100) –…

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Q: (f) If F¹(x, y) = 5y sin(xy)i + 5x sin(xy)j, then f(x, y) =

A: Given vector field F→(x,y)=5ysin(xy) i→ +5xsin(xy) j→ we need to find function f(x,y) such that…

Q: 13. The population of the town, rounded to the nearest whole person, remaining after 5 years is…

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Q: dy 3-t=8 dt

A: As per our guidelines we only solve one question and rest of the question will be reposted. Hint: To…

Q: 2. Set up a double integral using polar cor r=4sin 30. Do not evaluate. nates that will yield the…

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Q: Using a suitable trigonometric substitution, the integral dx 3 (16x² + 9)² is equal to sin 8+ C₁-<<…

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Q: O a. La función no tiene punto de inflexión. b.x = 1 & X = - 1 O.c.x = 1 d.x = - 1

A: We can find the inflection point as below.

Q: The limit is equal to 1/3/2 Select one: O True O False lim 818 3n² 2n² + 1

A: We can find the Limits .

Q: Specify the substitution you would choose to evaluate the integrals. S (t + 4) e²+8+1 dt Ou=t+4…

A: The given integral is ∫t+4et2+8t+1dt. We have to find substitution for the integral.

Q: an = 2 + (−1)n

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Q: Determine the area bounded by the curves y = ex, y=x²-1, x=-1, and x = 1. (A) 3.68 square units; (B)…

A: The region is bounded by the curves y=ex, y=x2-1, x=-1 and x=1

Q: 2) a) Let f(x) = 2* + 3x7. Find f'(x) and f" (x). b) Find the derivative f'(x) in the following…

A: a.)   Given f(x) = 2x + 3x-1/2 f'(x) , f''(x) are to be calculated. Formulas used here  ** y = ax…

Q: Evaluate ³*-2 dx 3x-2 e³x-2 + C O (3x-2) e³x-2 +C Ⓒ (3x-2) Ce³x-2 3x-2 3 + C

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Q: n=0 In(n + 4) n+4

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Q: k. y = 3x5 (5x+4)3

A: Use quotient rule to find the derivative.

Q: F(x, y) = (3x-4y2i+6yj by the force in moving a particle in the positive direction once around the…

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Q: Question 2 ( by the curves y = ) Draw the enclosed regio /1 1- x, y = 0 and x =

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Q: etermine the total differential of the function, f(x, y, z) = 2x³ + 5y¹ − 6z Odf = 6x² dx + 20y³dy -…

A: Please refer to the image below

Q: an+1 = √√42+ an, a₁ = −42

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Q: Find the general solution of the following differential equation. y" + 14y' + 50y = 0 NOTE: Use C1,…

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Q: Use differentials to approximate to 3 decimal places ( 1.09 ) 1/3

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Q: Use Stokes' Theorem to compute ff.xx where F = (x, xy, zy), and S is the upper half of the sphere x²…

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Q: 1₁ (²+4)y=12; y(0) = 0 (0) = 2 1.

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Q: Determine whether the following statement is true or false. — [√³] = √f'(x). dx If y = f(x), then

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Q: obtain the differential equation of: Circles with center on the line y = -x and passing through the…

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Q: n n2 + 1 Σ;

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Q: Consider the graph and determine the open intervals on which the function is increasing and on which…

A: From the graph of the function, we have to find its increasing and decreasing intervals.

Q: Which of the following geometric series are divergent? +00 +00 +00 ωΣ(5) «Σgn-1 α) Στ 3 n=0 n=0 n=1…

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Q: Let f(x) = (c + 1)x+ In(cos x). For what value of c is f'(/4)=6

A: This question can be solved using the concepts of differentiation.

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 − 4z2 = 21,    (−3,…

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Q: If the curve y = 4x², 2 ≤ x ≤ 5, is rotated about the x-axis, what is the integral that represents…

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Q: If the average value of the function f(x) on [0, 3] is equal to 3 1 3/² 0 what is Select one: 06 O…

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Q: i) Find the exact length of the curve 1 + 15 4x3 y = y = ii) Find the exact area of the surface…

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Q: Express the following sum in sigma notation. Use 1 as the lower limit of summation and k for the…

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Q: Σ n=0 3η – 2 5η + 7 +7

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