19. Any rational function of the form f(x) where b 0, always has a y-interce %3D

Q: 2x2 +13 5. S (1-x) (x2 +4) (++ z^)(x-1)

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Q: 20. Evaluate.d(x³ sinh(Inx)) O a. 2x3 − x O b. 2x² O C. 4x²-x O d. 2x2 − x

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Q: 7) Calculate the slopes of the following functions at the given points: Ta) f(x) = ln (x²-x + at IL)…

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Q: 4. Find the extrema of the function f(x) = Vx (x + 1) and the intervals on which its graph is…

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Q: 1. Find the definite integrals of the following functions : (a) L. 4.x dx (h) dx ex +1 -2 0. (b) /…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: For which x value does f (x) = x - 3x2 + 1have a local maximum. CO C-1 C 1 C -2 C 2

A: Given: The function fx=x3-3x2+1, To find: point of Local maximum

Q: Suppose that Mdx + Ndy 0 is an exact equation, and M and N are both homogenous functions of degree n…

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Q: 12 1 3. Find the exact value of the definite integral | dx (x+6) Vx- 3

A: The given definite integral can be evaluated using the method of substitution by making the…

Q: 1. Suppose that f f(x) dx = In x + Vx+1+C. Can f be a rational function? Explain.

A: To explain f is a rational function or not.

Q: b) Suppose x # 2. Find dif dx In y = In (x - 2)² √x² +1

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Q: 6. Determine the value of the constant a for which the function g(x) is continuous at x = 1 x2 + 5x…

A: This is a limit and continuity problem

Q: 4. If the integral value of | f (x)dx = 4 and | f(x)dx =-3 then the value of | f(x)dx is -1 -2 а. —3…

A: It is given that  ∫-14fxdx=4∫-24fxdx=-3

Q: 1-Show that the function defined by the base harmonic function f(x, y) = ex cos 4y

A: As per our expert guidelines we are allowed to solve only one question. kindly repost others. thank…

Q: 6 1) Find the general antiderivative for f(x) = 1+ x?

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Q: Let f(x)=4+ln(x2+3)f(x)=4+ln(x2+3) be a function defined on the interval [0,∞)[0,∞). Find the…

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Q: What is the maximum value of y = cos(0) for values of 0 between -720° and 720? O A. -1 О в 1 O C.0…

A: Given that: y=cosθ     and θ between -720° and 720°

Q: 9. DETAILS SCALCET9M 3.11.009. Write cosh(In(x)) as a rational function of x. Submit Answer View…

A: We can find the answer as given below

Q: Find the general solution using Reduction of Order: y''+y'=cos 3x

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Q: his question is designed to be answered without a calculator. = f(x) = 1-2e-x, then f has horizontal…

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Q: 9 Evaluate the integral f 2x (x² + 1)° dx using the substitution = x² + 1. и — с 2.x (x? + 1)° dx +C

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Q: Let f(x) = 16 ln( – x) + 4x + 13. (a) f'(x) = (b) Solve f'(x) = 0 to determine the critical values…

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Q: 11. Find two different antiderivatives of the function f(x) = 6x² +2ex. 1

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Q: Suppose that a y" + axy' + by = 0 has the general solution of the following form: y = x'(C1 cos (3…

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Q: 1 Find the most general antiderivative of the function x3 + 4x

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Q: Q2:- Apply romberg's method to the integral of f(x) = nx*cos(-Tx to 2 with Tol = 10-4

A: Given function is f(x)=14πx4cos14πx, we have to integrate above function from 0 to 2. Formula for…

Q: Suppose that Mdx + Ndy 0 is an exact equation, and M and N are both homogenous functions of degree n…

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Q: 1. Suggest ways to avoid loss of significance in these calculations. (a) √√x4+4-2 (b) ln(x+√x² +1)…

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Q: S de x² –2 x+1 A x2 --x - In Ix + 11 + C C x2 +x - In Lx + 11 + C B x² -x + In Lx + 11 + C x2 +x +…

A: Given ∫x2-2x+1dx. The objective is to evaluate the integral.

Q: Find the general solution using reduction of order. 1. y''+y'=cos(4x)

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Q: 3 f(x) = x° – cos(x) %3D х — - Solve this question by the Fixed-point method on the topic of…

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Q: 7. (4ea) Evaluate the definite integrals. a) L (3x2 + e*) dx

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: y" +y' = cos 3x

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Q: Show that for any ly ≤ 1 and|x| < 1. 1- xy 1-2xy + x² = Σ Tn (y)x" n=0

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Q: 1. Use properties of the definite integral to solve the following problem. f (x)dx = -3 and f(x)dx =…

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Q: 1(a): Find the value of k that makes function continuous at x = 4 4x +8 > 4 4x – k a <4 f(x) =

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Q: 23 Given f(x) = +1, that is defined over [1, 6]with a step (h= %3D 2+ sin(x) 1). Using the divided…

A: Given that, f(x)=2x32+sinπx+1 The NGF formula is, P2(x)=y0+q∆y0+q(q-1)2∆2y0 Where q=x-x0h Here…

Q: 8. Suppose that the tangent line to the graph of ƒ(x) = r0) at r = 1 is equal to the tangent line to…

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Q: For a. y′ =ln(y)+x,withy(1)=1. (Here x0 =1.) b. y′ =ln(1+y),withy(1)=0. (Here x0 =1.) Is it…

A: Solving for  a) y'=ln(y)+x            dydx=ln(y)+xdy=ln(y) dx+x dx Integrating:           ∫dy=∫ln(y)…

Q: [9] Find a 27-periodic solution u(x) of 5u"(x) + 3u(x) = f(x) where f(x) is a 27-periodic function…

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Q: On the interval (0,2n), the function f(x) = sin x cos x has critical points at: (A) x = 5m 3n 5n 7n…

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Q: 1. The range of y=-e* +2 is (-0,1). 2. The function f(x)=sin x+cos x is an odd function. 3. lim

A: Topic:- function  Topic:- as per our guideline only first three subparts need to be answered.

Q: 37 a)/ 2x cos(x) dx he right end-points with 4 sub-intervals) 1 b) -2x2+ X-4) dx 5.

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Q: Let k be a fixed positive integer. The nth derivative of 1/(xk − 1) has the form Pn(x)/(xk − 1)n+1…

A: Given: nth derivative of 1xk-1=Pnxxk-1n+1 Find: Pn1

Q: _4. If f(x) is any polynomial of degree 10, then the gth derivative of f(x) is zero. _5. If f'(0) =…

A: Topic = Derivative As per guidelines ,at  a time only three questions can be answered.

Q: 30. It is given that the graph of y=-x+mx-n touches the x-axis at one point. Suggest two pairs of…

A: Consider the following equation: y=-x2+mx-n The above graph touches x-axis. Substitute y=0 in the…

Q: 7. Find all values of x on the graph of f(x)=(x-1)´(2x+1) at which the tangent line is horizontal.…

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Q: (1) Locate the absolute extrema of the function on the closed interval. (a) y=4 sin x, [0,2n] (b)…

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Q: Where does x3 f(x)= х2 —1 have a critical point, which is not an extremum? O At x=-V3 O At x=-1 O At…

A: Second derivative test :  when a function slope is zero at 'x' , then the second derivative at 'x'…

Q: By the even extension method applied to the function f (x) = e-2", where x > 0, the value of the…

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Q: Find the general solution using Reduction of Order: x2y''-xy'+y=0 y1=ln x

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