How to determine whether the function is continuous or not at a given point x = a ? x ≤ 1 (3x5 - 1 x²-1 verify that the function f(x) = is continuous at x = 1 x-1 x > 1

Q: Find the differential equation of the family of circles of fixed radius r with center on the x-axis.

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Q: 3. (2 + y² + xy2) dx + (x²y + y + 2xy)dy = 0

A: As per the guidelines I can solve only one question

Q: ₁ x³ In x dx e 3

A: Solving the problem by finding the value of the integration.

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 6x²y²j

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Q: y = tan 2x 1-cot 2x

A: Given,            y=tan2x1-cot2xTo find : Find the derivative of the given function.

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

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Q: limn o 9-h-3 h 1 6

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Q: 2. Let f be the function from {a, b, c, d, e} to {1,2,3,4} with f(a) = 3, f(b) = 1, f(c) = 2, f(d) =…

A: givenf(a)=3f(b)=1f(c)=2f(d)=4f(e)=2

Q: The cos³4 dy is {A}-sin+sin³¹+C 3 4y 4 3 3 {B}sin-sin³¹+ C 3 4 3 (c)-sin-sin³+C {D}sin+sin³+ C

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Q: x +4 x²+2x+5 1₁ da

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Q: 8. eeer +eyty dy

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Q: Determine a for each arithmetic sequence. See Example 5. 33. as = 27, as 87 www 34. α12 = 60, 920 =…

A: A detailed solution is given below

Q: Je-2x sin 2x dx

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Q: 10. x*(lnx + 1)8** dx

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Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

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Q: COS X 6. y = x What is the appropriate formula? dx Solution:

A: Given query is to find the derivative of the expression.

Q: Set up the integral to find the area of the region bounded by x = 4y - y³ and x = 0.

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Q: The f2e4t sec2e4t dt is {A} = = tan e 4t + C {B} = sec³e4t + C 16 {C} /e4t tan e4t + C {D} et…

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Q: 6. 22x+x dx

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Q: Consider the function f(x) below. At what value(s) of x are the inflection points? Enter answer…

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Q: y = = Ax is YBC Ycs YBS = 1 -1 0 1 1 0 - D IB XC IS

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Q: Determine whether the series converges or diverges. 4n³ n²-4 n=2

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Q: Use a graph to estimate the coordinates of the lowest point on the curve x = t³ - 31, y = 1² +1+1.…

A: Consider the parametric equation x=t3-3ty=t2+t+1 Sketch of the parametric equations is shown below.

Q: Σ n=2 7 n(In(n))*

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Q: The radius of the base of a right circular cone is decreasing at the rate of 4 cm/min, and the…

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Q: Use the simplex method to maximize the following: Maximize f=6x1+4x2+10x3f=6x1+4x2+10x3 subject to…

A: We need to use simplex method.

Q: 3. Evaluate the double integral: ²₂2(x+3) dy dx 4. Evaluate the triple integral: ₂ dx dy dz Z

A: Topic:- multiple integration

Q: a²z a²z Determine + Ər² მ02 if_z = tan-¹ Ө - r + r r²+0²

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Q: Question If a brick is dropped from a height of 40 ft., its position after t seconds is given by the…

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Q: 2. dx ***S 1 - x4

A: Integral

Q: If F(x) = f(t) dt, where f is the function whose graph is given, which of the following values is…

A: F(4) is the answer.

Q: For items 1-5 A 10-ft ladder is leaning against a house on flat ground. The house is to the left of…

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Q: Write an equation of the form y=a sin bx or y=a cos bx to describe the graph below. 0 3 2- AA. - 2n…

A: Write an equation of the form y = a sin bx or y= a cos bx to describe the graph below.

Q: Find the laplace transform of f(t) = 6t³ + 4t² 3 F (s) = F (s) F (s) = F (s) = F (s) F(s) = -85³ +…

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Q: Evaluate the limit A. ƒ(x) = 5x + 2 at x = 3 x²-9 B. f(x) at x = 3 x-3

A: A. f(x)=5x+2B. f(x)=x2-9x-3

Q: 5, i, Evaluate the first and second derivatives of the function z=2x4+3x3+2x-5 when x = 4.

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Q: 12. y = −3 cos (0 + 1) − 2 Amplitude: Period: Phase Shift: Midline:

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Q: Question 10 Given: y = xcos (x); Find y'". O(E) None of these Oy" xsin (x) + 2 cos(x) Oy" asin (x) -…

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Q: Evaluate: sec²(4t) [3-tan(4t)]³ dt a.-16 [3-tan(4t)] + C b. | [3 –tan(4t)] + C 4 OC. 1 [3-tan(4t)]…

A: integration

Q: valuate the triple integral ***"* sin² (z)ze-²v³ dzdyda

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Q: a. f(x) = on [-1,4] 1²+2 b. f(x) = I√4-1² on [−1,2] c. f(x) = 2 sec r - tan r on [0,1]

A: At the  extremum of a function f(x), the first derivative is zero.

Q: If ả = 2ỉ + 33, b = j – ỉ and ở = 33 are vectors in 2D, then determine the of a + 3b + c

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Q: Evaluate the following 2- S ( 37/3 + 5x² + 3) dx

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Q: 7. ft³10t+-3 dt

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Q: 11. f²(2x - 3) dx 12. ²₂(x³ + 2x) dx 13. f(x² – 2) dx

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Q: Evaluate fi fi fi (xy+z)dxdydz Note: input your answer in two decimal places (example: 1.05, 2.53,…

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Q: Find a Cartesian equation for the curve and identify it. ² cos(20) = 1

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Q: Find the volume of the solid that results when the region bounded by y = x and y = x², from x = 0 to…

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Q: lim (cos(9x)) (+) x-0+

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Q: Write down the matrix A that represents the linear transformation ƒ : R² - (a) R² (i.e. so that f(x)…

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