2. If a function f(x) is differentiable at x-a, then function f(x) is continuous at? А. х-а В. х-х С. а-х D. f(x) 3. The operation of finding the derivative of a function is called? A. Differentiability B. Continuity C. Differentiation D. Differentiability and Continuity 4. What is the derivative of a constant? А. О В. 1 С. -1 D. x+y

Q: x² dx J (² – 25)5/2

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Q: The projection of the vector 21+3ị – 2k on the vector i-2j+3k is 2 14 V14 1 V14 O None of the…

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Q: at is the area enclosed by the curve r = 2 cos 36? wer is in square units. Use two (2) decimal…

A: To find the aera.

Q: 2 f(x) ; а3D0, Ь%3D1 1+ x %3D

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Q: f(x) = x²+2x+1 g(x)= x+3 Set up the integral to find the area between the two curves. 1 -3 -2 -1

A: We have to find area bounded by the given curve.

Q: The task is to determine and sketch the domain of the function In (b – a? + 4) g(a, b) = V36 — 4а2 —…

A: We have to determine and sketch the domain of the function.

Q: What is the area of the region bounded by the graphs of y = x and y = x°? Answer is in square units.…

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Q: Osyt . yrosx

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

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Q: 10. Calculate the area of the shaded region bounded by the curves y = 1+4cos'x and y=-sinx, as…

A: From the given figure to find the area enclosed by the given region is bounded by the above from…

Q: IV. Determine if the given is convergent or divergent. n Σ #2. (n² + 1)2 n=1

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Q: > (atan (2n – 1) – atan (2n +3)) n=0

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Q: Write the standard form of the quadratic function whose graph is a parabola with the given vertex…

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Q: 1. Sketch the region enclosed by the given curves: y = e*, y = x² – 1, x = -1, x = 1. Find the area…

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Q: 4. A1 y = 2x 2+ A1+ A2 = A3 1+ y= x2 482

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Q: Using homogenous differential equation determine the particular solution of

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Q: The antiderivative of [Vx-25 dx is V x2 - 25 - sec-x+ C. A True B False

A: Given: I=∫x2-25xdx     As we know from the trigonometric identities; 1). sec2x=tan2x+1 2).…

Q: Vy x+y Q3) Evaluate triple integral SN S dz dx dy. x-y

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Q: 5) S dy 5.)

A: The given integral,      ∫28-y2dy

Q: Convert dzdydx Into an integral of cylindrical coordinates 45 hardzdrde Option 1 Option 2 Option 3…

A: To convert the given integral into cylindrical coordinates.

Q: 1 Given the function g(a, b) = g(a, b) where suppose m %3D a²b+b a = cd b = c3 + 6d %3| дт The task…

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Q: Find f(100)(x) if f(r) = (x + 2)100. a. 0 c. 100! = 100 x 99 x 98 x 97 x ... x 2 x 1 b. 100 d.…

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Q: If sin theta is square root of (x^2 - 4), what is sin 2 theta?

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Q: If f(x)=2x²- xª, then f(x) has... Jika f(x)=2x²- xª , maka titik ekstrim relatifnya adalah.... 1. O…

A: f(x) = 2x2 - x4 we have to differentiate function and find points f'(x) = 4x -4x3 f'(x) = 0 4x -4x3…

Q: ( 3x2 + 1, { if r 3 а. —8 b. -18 с. 18 d. does not exist

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Q: What will be the output of the following code snippet? #include int main() { int a = 3, b = 5; int…

A: Here is the solution

Q: Given: an = In(n + 1) – In(n) for n e N Determine if the following is convergent or divergent. (a)…

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Q: Suppose f(x) is a function that satisfies the following conditions: f(15) = 20, f' (15) = 2. Also…

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Q: Find the general solution of 2x². 2² + y? dx Find the general solution of (2x – y) dy 2y – x d.x dy…

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Q: Find the sum of the convergent series. +0 | 3n+1 6n-1 n=0

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

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Q: The plane N contain the points P(1,–4, –5) and Q(2, 1, –3). Moreover, it contains the line 1 3 -x =…

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Q: Determine the sum of the following series. (– 4)" -1 6" n=1

A: To find the sum of ∑n=1∞ -4n-16n   ∑n=1∞ -4n-16n = -41-161+-42-162+-43-163+-44-164+....⇒∑n=1∞…

Q: FALSE if otherwise. Prove your answer. (b) If the power series > an(x + 1)" converges at x = 2, then…

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Q: 1 In solving the antiderivative of f(x) = 2- 3sin(x) by miscellaneous substitution, the substitution…

A: Given: fx=12-3sinx To find: ∫f(x)dx We know that, sinx = 2tanx21+tan2x2

Q: Use the triple integral to find the volume of the given solid. The solid enclosed by the paraboloid…

A: Use the triple integral to find the volume of the given solid. The solid enclosed by the paraboloidx…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: 6x – 8x² – 5 · dr (2r – 1)(4r² + 1) (c)

A: Student has specifically asked for the solution to the Question(C). Hence that problem is answered…

Q: f(x) = 2"[In(cot(x³))]5

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Q: If a function f(x) satisfies the inequality 5 cos(2x) < f(x) < 8x2 + 5, what is the value of lim,0…

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Q: Evaluate the following sum of iterated double integrals: -2у 2 •4–2y dr dy + | dx dy 0.

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Q: Q4) Find plane area inside the polar function r = 2 and outside the polar function r = sin e) +1 in…

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Q: п(х — 2)" 3" (2n – 1)3* VI. Consider the power series n=1 a. Show that the power series converges…

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Q: Find the sum of the convergent series tan - ( m til tan M=1

A: This is a telescoping series.  Whose sum is  2/π

Q: Determine whether the following series is convergent or divergent full solution pls and write what…

A: The given series,          ∑n=1∞3-n4n34

Q: The region R is bounded by the curve with equation y = sin 2x, the x-axis and the lines TT x = 0 and…

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Q: Solve the following equation: 16ª = 8ª+1 O 3 O-3 O 1

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Q: (-1)"n" sin" () Σ n 2n n=1

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Q: 2. Apply the eigenvalue method to find solve the initial value problem: (a) x = 3x, + 4x2 x = 3x, +…

A: Given a system of differential equation  x1'=3x1+4x2x2'=3x1+2x2x1(0)=x2(0)=1 As per our guideline,…

Q: Determine whether the following series is convergent or divergent 3- Vn (a) 2 n=1

A: The given series is: ∑n=1∞3-n4n34,an=3-n4n34, n≥1f(x)=3-n4n34