To evaluate dx using trigonometric substitution, which of the following is the new integral form in term of 0? A sin 0 cos? 0 dO В sin? 0 cos? 0 de (c) None of the choices D cos? 0 d sin? 0 d0

Q: Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x)…

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Q: Compute the given integral. dr 16x2 + 1 +C

A: Here is the solution:

Q: 4. x2(y + 1)dx + y² (x – 1)dy = 0

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Q: Using Integration By Parts, x3 x2 +4 dx = uv- - Sv du

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Q: x³ + 6x² + x+2 s ax + In[cx + 1}*(x² – x + 1)°| + fx-1 Tan-1. V3 The resulting integral of x³ +1 +…

A: use simple integration formula.

Q: Express the limit as a definite integral on the given interval. 5 V 3x; + (x;) Ax, [2, 3] * lim n →…

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Q: The part of the sphere x? + y? + z? = 16that lies between the planes z = -2 and z = 2. (Enter your…

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Q: Question 7 15х2—х3— 43х — 19 Ax+ B C D -dx can be rewritten as dx. The integral + + (x+1)2(x2– 6x…

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Q: Consider the statements: P:= Today is Monday. Q:- Amy has no classes. R:= Tomorrow is a busy day.…

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Q: 9х2— 6 To evaluate dx using the method of partial fractions, the given integral can be rewritten as…

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Q: (2x + 4) + 1 (2x +4) +1 dx: x2 + 4x + 5 x2 + 2x- 10 2 2 2 Consider dx = x2 (x2 + 4x + 5) dx evaluate…

A: We can solve as follows

Q: A company manufacturers and sells a televisions sets per month. The monthly cost and price-demand…

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Q: Assuming that z is a function of x and y, find the equation of the tangent plane and the equations…

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Q: Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = In(x2 + 3x…

A: I am attaching image so that you understand each and every step.

Q: Evaluate the integral 8) da 21 3-8. by making the substitution u = NOTE: Your answer should be in…

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Q: Find the partial derivatives of the function V1r2 + 1s² + 6r² w =

A: Given,  w=1r2+1s2+6t2

Q: Consider the following function and closed interval. f(x) = x3 - 4x2 – 16x + 5, [-4, 4] Is f…

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Q: g(t) = 2t3 + 3t² – 12t %3D Find the intervals where g(t) is increasing and the intervals where g(t)…

A: Given: gt=2t3+3t2-12t   (a). To calculate the interval for increasing function, g't>0

Q: 2x+11 3. 1 dx, evaluate Consider 3 x² + x – 6 = xp dx X+3 X- 2 X+3 X-2 |(x- 2)° +C In x+3 x-2 In +C…

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Q: Tutorial Exercise A population of a particular yeast cell develops with a constant relative growth…

A: Let's find.

Q: o and lim g(X) J(X)g(X) is always 0.

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Q: dx Using Trigonometric Substitution J- 4 sin 8+C express the answer in terms of x. (x²+ x + 1) ² 4x…

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Q: 12x²-x² * x+2 dx= D dx • x +1 Consider dx = ,find A+B+ C+D· x4+ x3

A: Consider ∫2x3-x2+x+2x4+x3 dx=∫Ax+Bx2+Cx3+Dx+1 dx, then to find A+B+C+D.

Q: Find the velocity and acceleration vectors in terms of u, and ug. r= a(6 + cos t) and 0= 5+ e where…

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Q: The plane y = 1 intersects the surface z = x° + 5xy – y* in a certain curve. Find the slope of the…

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Q: sec(6z)tan(6x)dx, u = 6x

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Q: Consider - x2 + 2x - 10 2 (2x + 4) + 1) dx · evaluate x² (x² + 4x+ 5) (2x+ 4) +1' dx - x2 + 4x +5 x2…

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Q: dx + (1 – x²)cot y dy = 0

A: Given problem :- dx + (1-x2 )cot(y) dy = 0 Find the general solution of given differential equation

Q: Determine whether or not the vector field is conservative. If it is conservative, find a function f…

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Q: What will you factor out from the integrand of tanx sec'x dx so that you can transform it to its…

A: To factor out a term such that the given integrand becomes integrable.

Q: Question 1 Consider / sin*x cosºx dx. f we let 4 = sin x, the integrand can be transformed to, (B ®…

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Q: x³ + 6x² + x +2 dx? How many quadratic and distinct factors are in the denominator of x³ +1

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Q: Find the antiderivative F of f that satisfies the given condition. Check your answer by comparing…

A: ∫f(x) dx=∫ 5-31+x2-1dx=∫ 5dx-∫ 31+x2-1dx=5x-3arctanxAdd a constant to the solution=5x-3arctanx+C…

Q: Find an antiderivative of the function. (a) h(q) = sin(q) H(g) = (b) f(x) = 3eX F(x) =

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Q: 3r + cos r 2. Use Squeeze Theorem to evaluate_ lim 1-00 V1 +r2 - 5x

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Q: Find the length of the following curve. If you have a grapher, you may want to graph the curve to…

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Q: x2 dx is F(b) – F(a). where F(a) and F(b) are real numbers. What is the value of F(a)? The result of…

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Q: Ca

A: ∫92-x22dx=∫81-x22dx=∫ 6561-162x2+x4dx=∫ 6561dx-∫ 162x2dx+∫ x4dx=6561x-54x3+x55Add a constant to…

Q: lim(8x + 16) = 24 Use the epsilon-delta definition of limit to prove that æ→1

A: Let's find.

Q: f2x² Find uv- v du Using Integration By Parts, dx =uv- du UV- | S12 xe 6 x2 dx 3 x2 6x e dx 02

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Q: 1. 4x dy – y dx = x²dy %3D

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Q: sec(3r2 + In 2) evz+2 +9 a. y =

A: Use simple differentiation formula.

Q: Compute f'(a) using f' (a) f(а + h) — f(a) = lim f(x) or f'(a) = lim f(a) for f(x) = 10x³, a = 2.…

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Q: cos2x – sin2x cos2x dx = For -F(x)+C What is F(x)? cosx – sinx 2 2 sinx + =cos'x+cosx + =sin³x 3 3 2…

A: For ∫cos 2x-sin 2x cos 2xcos x-sin x dx=13Fx+C, to determine Fx.

Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y…

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Q: Find the first partial derivatives of the function. f(x, у) = 3x + 5y + 4 fy fy

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Q: Find the derivative of y with respect to t. y = In (t) dy %3D dt

A: Given function y=lnt9 we have to find derivative of y with respect to t. ln is natural logarithm…

Q: 3. Evaluate the lim(2x – 7). x-4 а. lim(2x — 7) %3D 2 x-4 b. lim(2x – 7) = 1 с. lim(2x - 7) %3D7 x-4…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: As a group, discuss why there are no terms of the form x*, xy, or xy in the expansion of (x+ y)'.…

A: (1) In the expansion of (x+y)3, each term has the power 3 ,that' why x4,x2y2,xy  do not exist

Q: Find the point(s) on the graph of f where the tangent line is horizontal. f(«) =x°c* (0, 0), 9, 99…

A: We need to find points where tangent is horizontal.