2 +3 Evaluate S4) (-2) (22+4)(- dx. Enter In(x) for In(x), abs(x) for |x|, and arctan(x) for arctan(x).

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A: Integration by parts is used to integrate an expression that is a product of 2 functions. The…

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A: Note :As per our guidelines we are supposed to answer only one question if there are multiple…

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Q: 1.) Given that dy/dx = ∛(x^2 ) and y=3 when x=-1, find the function f(x) in terms of x 2.) Given…

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Q: sin(4-y)sin(3-y)dy

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A: Given- x2 + 2x - 3e-x - 1cos2x; use interval 0, 1  To find- Find the root using the Secant Method

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A: Consider the mid-point rule on the interval [a, b] for approximating

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

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Q: sinh (iz) = i sinz sintiz) =isinh z,escia)= cosh: 2. !!

A: In this question, the concept of a trigonometric function is applied, Trigonometric Function The…

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A: Residue theorem

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Q: terentiation 2 2 Find dy if y=x'+ sinxy 1.

A: Since you have asked multiple questions, as per the guideline we will solve the first question for…

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A: Last option is correct.

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A: The graph of sin 3x is continuous on the entire number line.

Q: Teste for conitinuity of the foll dwing f1x) = + 42 -1 2- f x)= d 4 - z2 3- frx) = 2ォー ズ+

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Q: SIMPSON'S USE N=6 ACTIVITY # 8 : esinx dx SOLVE USING TRAPEZOIDAL AND SIMPSON'S RULE

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Q: Applying the Trapezoid Rule Approximate x² dx using the Trapezoid Rule with n = 4 subintervals.

A: Trapezoid Rule: Trapezoid rule for approximating ∫abf(x)dx is…

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A: Given:        ∫-111 - 12x dx   To find the value of ∫-111 - 12x dx   Formula:          ∫xn dx = xn…

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Q: In the function given (108). Evaluate the integrals.

A: given ,fx≥0 on0,2 ,  f(x)≤0  on 2,5∫02f(x)dx=6  and  ∫25f(x)dx=-8 we have to find ∫25f(x)dx

Q: tanx -√ S sec²x 1+ et tanx In (secx) √✓ 1+tan²x 1+ elanx sec ³x 1+etanx If f(x) = A B (с 1+1² 1+e'…

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Q: Find the limits

A: Consider the provided expression, limx,y→0,4xy Find the limit of the provided expression.

Q: 10 If f (x) dx -7 and f (x) dx = 1 then determine -3 -3 10 [1- f(2) dz 5 showing working.

A: Given: ∫-35f(x)dx=-7 and ∫-310f(x)dx=1

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A: We will find the limit

Q: rpression in r, for x > 0 /9 - x2 5. CSC arctan PACE

A: Let theta = arctan(sqrt(9-x^2)/x)Form there find tan theta

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Q: Derivatives: using (4 step rule). 4. f(x)=sin3xcos3x 5. f(x)= x² cos(x² +1)

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Q: Using integration by parts, evaluate x cos(3x) dx x cos 3x - sin 3x + C Option 1 x sin 3x - cos 3x…

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Q: Ci-2)x OS how that dx = where cis constant of integratron abore or Otherwise Using find f ansurer -2…

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Q: 2. tanh x (12) tanh(2x) = %3D 1+tanh x

A: Answer

Q: i. y = sinh-1 (x), ii.y = cosh-1 (x),x > 1 iii.y = tanh-1 (x), |x| < 1 %3D

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Q: 2. Using contour integration and the residue theorem show that: dx x4+1 2/2

A: Applications of resiuce theorem

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A: Given,             fx,y=sin2x3+3y35330x2+2665y2x,y≠0,00x,y=0,0

Q: lim 0 2 + sin(okr }) k=1 6 O A. J(x + sin(2xx)) dx 6 O B. J(2x + sin(2xx)) dx 3 O C. J(x +…

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Q: x3 dx Using integration by parts to solve J- V4-x2 and letting -÷x², then v = f(x) is U = - %3D

A: We use integration by parts

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Q: O lim メーや 2X-5 /メ -V-オ-2 V x +3 ar conditioning. メーろ 2-x2 ulim メー→/2 | lim 4) "Sina-Cosxsinx; メーO…

A: a.limx→42x-53=2×4-53=1 b. limx→-3=x+4--x-2x+3since numerator is not zero, while only denominator is…

Q: R= {y = x^3 + 1, x=1, x-axis}   Can you help me answer this? And explain how did you get the…

A: Solution) R= {y = x 3 + 1, x=1, x-axis} We find the intersection point  y = x3 + 1 When  x = 1 y =…

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Q: FINO THE PARTICUCAR SOUTUON OF THE DIFFERE NTIAL EQUATION -スx =e + hx t子x-9 dx² -2x dy e AT X=0,9=0…

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Q: uestion 4 .2 F(x)=f(x) and F(– 1) = F(2)= -5, then f(x)dx= -1 If

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Q: 3x+2 b. Evaluate dx, using a suitable technique and provide the reason for -2 (3x²+4x+2)* your…

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Q: lim sin(2z) = z-/3 %3D /3 2. 1/2

A: We need to find limx→π3sin2x