- f(æ) = Where is %3D discontinuous? x2 + 3x – 18 - o f(x) is continuous everwhere O 3 O-3 and 6 O-6 O -6 and 3

Q: The maximum value of x + y + z subject to the constraint x² + y² + z² = 1 is Write in decimal form…

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Q: Arcsin(x/y) = 4x + 3y

A: To find out the double derivative.

Q: = a and log5 2 = b then log5 216 can be expressed as pa + gb. The value of (nearest whole number)…

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Q: Determine whether the series converges or diverges. cosº (n) n² + 5 O converges O diverges

A: Here, the given series is: ∑n=1∞cos2(n)n2+5 Let, an=cos2(n)n2+5; n≥1

Q: convergent or divergent. Please provide detailed solution. a) : E 10" n=1 (n + 1) 52n + 1 00 -5n 2n…

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Q: Find the curve length of the function 1 1. f(x) = ;x² 0 < x < 3

A: We can find the curve length as below.

Q: Given f(x,y, z) = In(x² + y² + z²), show that ² f , ²f , ² f x² + y2 + z2

A: Given problem:-

Q: Find the angle of the largest right circular cone which can be inscribed in a sphere of radius 9…

A: Given problem:- Find the angle of the largest right circular cone which can be inscribed in a sphere…

Q: Question 2 - a) [i- :- :]: Explain why the following series (-1)" 1+ n3/2 n=1 is Alternating. ]: Use…

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Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

Q: Using appropriate trigonometric substitution, dx XV9 — х2 is transformed to

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Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: Solve the given equation for x. 420-4 = 39 You may enter the exact value or round to 4 decimal…

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Q: Solving by variation of parameters y" – 3y' = x the general solution is: None of them c_1+c_2…

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Q: Prove: If s S6sn for all n EN and if both sn Land un+ L, where LE R, then t - L asn- 0 as well. That…

A: We are given that sn≤tn≤un  for all n ∈ℕ and both sn and tn converges to L∈ℝ.We need to show that tn…

Q: 6. Figure out the following limits without applying L'Hopital Rule. sin(r- 4) V2r -1-1 b. lim (2²…

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Q: Find the slope of the function f(x) = V5x at x = 5. V5/2 -25/2 1/2

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Q: Without evaluating the constants, the partial fraction decomposition for 5x? – 3 - f(x) %3D (x3 –…

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Q: is equal to sec (2x) + In|sec(2x)|+ C sec (2x) – In|sec(2x)| + C the above the above Gsec (2x) –…

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Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: Find your answer below

Q: Change from cylindrical coordinates to rectangular coordinates 0 =- 3 O None of the others O y = -3…

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

Q: Eliminate the parameter and find à corresponding rectangular equation: x = t , y = 2–3 t

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Q: Using the method of undetermined coefficients, a particular solution of the differential equation y"…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: The solution y, of the homogeneous differential equation y(4) + 36y" = 0 is None of them c_1+c_2…

A: We have to find solution

Q: The functiion?n f(x)=/x) is odd or even?

A: Explanation of the answer is as follows

Q: An angle Θ is known to vary periodically with time, in such a way that its rate of change is…

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Q: Which of the following is the particular solution of a nonhomogeneous differential equation…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost the…

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

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Q: the Area that lies inside r=3+2 sin 0 out side r=2 is

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Q: Express the limit as a definite integral on the given interval. -Дх, [1,4] (x;)2 + 9 lim i = 1 dx

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Q: Evaluate the limit using L'Hospital's rule 1 - 10x lim 10xe -

A: Given query is to find the value of the limit.

Q: The indicial equation of the differential equation x²y" + (x2 – 3x)y' + 3y = 0 about the regular…

A: Given

Q: Solving by variation of parameters y" + 2y' + y = e*the general solution is: c_1 e^(-x)+c_2…

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Q: | 4.5x + 3.2y = 7.7 0.8y 0.9x 0.1

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Q: The solution of the Ordinary Differential Equation 4y" - y' - 3y = 0 if y(0) O and y'(0) %3| 7 - is:…

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Q: The mean of two samples of size 50 and 100 are 54.5 and 50.3. Calculate the com bined mean of the…

A: Topic:- Basic algebra

Q: Find the Area bounded by the given curves. y = 2x + 1 ,  y = 7 - x ,  x = 8

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Q: Given f(x) =x2- 1, find the value f(p).

A: Given: f(x)=x2-1

Q: 3x2 – 2x – 8 - Let f(x) 3x2 – 11x + 6 - This function has: 1) A y-intercept at the point 2)…

A: Simplify the function using definition of asymptote.

Q: Let f(x) = log2(x) and g(x) = cosx. Give the composite fog and go f, and determine their domains.

A: The given functions are: f(x)=log2(x) &amp; g(x)=cos x

Q: Using appropriate trigonometric substitution, dx xV4 – x² is transformed to S sin 0 d0 sec 0 d0 2 2…

A: The detailed solution is given below Thank you

Q: Let E be the region that lies inside the cylinder x2 + y2 = 64 and outside the cylinder (x- 4)2 +y2…

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Q: solve the following first order differential equations (Homogeneous Equations)

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Q: Solve the second derivative(y") of the following function and simplify the final results. Show your…

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Q: Find the value of the derivative (if it exists) at the given extremum. (If an answer does not exist,…

A: f(x)=(x+5)23  f'(x)=23(x+5)-13  f'(x)=23 (x+5)3Let's understand f'(x) as a different…

Q: Using appropriate trigonometric substitution, dx J xV1 - xV1 – x2 | is transformed to

A: Topic = Integration

Q: s required to repay a loan that matured to $4,550 on August 14, 2015. ne realized that he could…

A: Topic:- simple interest

Q: 4 about the point a = 3. (Your answers should include the variable x when appropriate.) Find the…

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Q: I. Find the equations of the horizontal and vertical Tangents. x3 + 3x? – y? = 0

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Q: Express the limit as a definite integral on the given interval. lim n- 00 [4(x;)³ – 4x;"]ax, [(2, 7]…

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