Using the substitution u = expressed as an integral in terms of u is given by -1, the definite integral 5 2 2 ° 1² ( ² 0²² - ²3 0²²2 +4 201²/²) + 5/2 -u³/2 +2u¹/2 du 2 3 (5² +2³2 +0³/²) du (25/2 L₁ (125/2. 4 ° /* ( ²3 0²/²2 - 03/1²/²2 + 201¹/²) du [₁₂ x²√x - 1 dx (u5/2+2u³/2+u¹/2) du

Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

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Q: ax+ 2 x ≤ 2 f(x)=4-x², 2<x<3 2x+b. 3 < x Find the value of a so that f(x) is continuous at 2. Find…

A: To find out the value of a as f(x) is continuous at 2.

Q: Solve the given dy=x√ e+~

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Q: Inverse functions Let f(x)=11x+10   Find f^−1(x)  f^−1(x)=

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Q: Find where it increasing and decreasing x^5-2x^4+3x^2-5x+

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Q: 8x³ - y³ 3 lim (z,y) (1,2) 2x - y Select one: O equals 12. O equals 0. O None of them O equals 4. O…

A: Lim(x, y) -(1,2)(8x3-y3)/(2x-y).

Q: Find the limit of the following sequence or determine that the sequence diverges. 2n² 1 6n² + 1 -…

A: Solve the following

Q: (4x² - 9)72 99

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Q: A square is increasing in area at a rate of 20 mm² each second. Calculate the rate of change of each…

A: topic- application of derivatives

Q: For the curve f(x) = Find the horizontal and vertical asymptotes. x-4x² +2 x² - 4x +4

A: This question can be solved using the concept of horizontal and vertical asymptote of rational…

Q: converge

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Q: Region A is bounded by the parabola x = y², the line y = 1, and the y-axis. Region B is bounded by…

A: As per the instruction, we will be answering the first question. Given: We need to find the volume…

Q: Explain why the vectors u₁ = (2, 4,-4) U₂ = (-4,-8, 8) form a linearly dependent set of vectors in…

A: To find the reason for the given vectors to be linearly dependent.

Q: Evaluate the limit: lim, ∞ ○-6 00 ○ 6 e 10-00 최승

A: This question can be solved using the concept of L hopital's rule.

Q: For the limit, lim (x,y)→(0,0) sin(x² - y²) x² - y² if we approach along y-axis, we will get 1.…

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Q: The temperature in degrees Celsius on the surface of a metal plate is given by T(x, y), where x and…

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Q: Let f(x) = = √9 - x + 5. Determine f-¹(x) and the the domain of f¹(x). ƒ-¹(x) Domain of f-¹(x) = =…

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Q: A particle is moving with acceleration a(t)=30t+8a(t)=30t+8. its position at time t=0t=0 is…

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Q: Find the volume of the solid generated by revolving the region between the parabola x=y^2+1 and the…

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Q: Question a) b) Let f(x, y) = 2√x - y²e-2xy Find fx and fy. Evaluate fxxy(4,-1). + NIA

A: Given :fx,y=2x-y2e-2xy+2y

Q: ZOOM Find the following for each problem: a) domain, b) x-intercept(s), c) y-intercept, d) vertical…

A: According to our guidelines, we can answer only one question or three subparts of a question. Other…

Q: The limit lim (x,y)→(4,-5) exists and equals to Select one: O True O False 25x²-16y² -5x-4y -40

A: Given the limit is  limx, y→4,-5 25x2-16y2-5x-4y.

Q: Use a triple integral to find the volume of the solid bounded by the graphs of the following…

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Q: he domain of the fur

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Q: If f(x, y) = Select one: O None of them In (x² - y) then the domain D of the function f is given by…

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Q: Let the function f(x) have the property that f'(x) = ¹.1f g(x) = f(x²) find g'(x). g'(x) = Solution:

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Q: If f'(1) = 4, f(1) = 2, and g(x) = f(x) tan-¹x, what is the slope of the tangent line to the curve y…

A: Here we have to find the slope of the tangent line.

Q: a) Find the integral / r(t)dt. b) Find parametric equations for the tangent line to the given curve…

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Q: Evaluate: 0 tan-¹ (0) de arctan(0)—0 2 giarctan0+ + C arctan0+ arctan(0)–0 2 -arctan0+C 0–arctan(0)…

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Q: Consider the function f(x)f(x) whose second derivative is f''(x)=9x+9sin(x)f′′(x)=9x+9sin(x). If…

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Q: Use the Integral Test to determine whether the following series converges after showing that the…

A: If f(x)  is a continuous, positive and decreasing function on the interval [k,∞)  and  f(n)=an…

Q: Numerically estimate the slope of the line tangent to the graph of the function f at the given input…

A: W need to estimate slope.

Q: Find a parametric description of the line segment from the point P to the point Q. P(0,0), Q(22,-26)…

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Q: Evaluate: 12+3 2√x+3 ○1-3 ln (7/5) O2-3 ln(7/5) 2 O2+3 ln7 03-In()

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Q: Question interval [0, 12]. Select one: True False If f(x, y) = 3√/16 - x² - y2, then the range of f…

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Q: Evaluate: St dz 2√√7+3 ○1-3 ln(7/5) O 2-3 ln(7/5) 2 2+3 ln 7 03-In()

A: Given :∫14dx2x+3

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² - 2xy + y²,…

A: Given that   f(x,y)= z = x2-2xy+y2     So,  this can be rearrange as…

Q: z = (x + y)², x = s²t, y = st². Use the Chain rule to find dz for t = 1 and s = 2. ds

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Q: Question 43 What is the horizontal asymptote of y= (x - 1)e-2? O y = 0 to the right O there is no…

A: topic - Horizontal asymptote of a function Line y=L is a horizontal asymptote of the function y=f(x)…

Q: Evaluate f cosh² x dx đ (sinh 2 từ t + x) + C O 2r O2e² +42 + C 8 O None of the choices…

A: We have to evaluate  ∫ cosh2(x) dx

Q: Assume mmh (x) = f(g(x)) such that the first an exist g Second derivatives of both of and What is b"…

A: Assume h(x) = f(g(x)) such that the first and second derivatives of both f and g exist  We have to…

Q: lim t→∞ 14/3 + 71/3 2 (6+²/3 +11) ²

A: To find out the limit.

Q: lim x-x6-x O +∞ 00 ∞- O O 3 1 2 ||

A: topic - limits

Q: Work problem 3 Given the vector function F(1) = (51³ — —, sec —7, sec(3 − 1)) - then find the…

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Q: Apply Newton's Method to f(x) and initial guess xo to calculate x₁, x2, x3. f(x) = x³ - 19, xo = 3…

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Q: Find the limit of the following sequence or determine that the sequence diverges. {tan - 1 (₁ -1…

A: Here we have to find the limit of a sequence.

Q: Numerically estimate the slope of the line tangent to the graph of the function f at the given input…

A: Given function :- f(x) =3√x  Estimate f'(1)

Q: dy Find using implicit differentiation. dx Hint: First clear the denominator to get 8x² + 6y =…

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Q: Find the arc length of the following curve on the given interval. x=7t+1, y = 24t-7, 0≤t≤3 The…

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Q: Let z = √√√7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2. ds

A: To find out the given partial derivative.