Find thu constont a on b Such that the Sinclion is continuous on the entire X2-3 fex) ax+b, -34X24 -1, real linu. a=

Q: Where is the function f(x) is continuous, such that f (x) : In(1-2x)+sin (x 4x+3 %3D [-1, ] – (-) O…

A: We know, ln(x) is defined for x>0. sin-1(x) is defined for x∈-1, 1. f(x)g(x) is defined if…

Q: glay). ty sin Ctg) if مره( - إد x( %3D

A: Given that gx,y=x2+y2sinx2+y2    if x,y≠0,0a                     if x,y=0,0 To find the value of a…

Q: Evaluate the integral. ∫0 π/3 tan5 x Sec4 x dx

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Q: Find the intervals where the function f(x) = 2cosx + 1/ sin2x, 0≤x≤ 2π is concave up.

A: Let's solve.

Q: Use integration by parts to show that, for n > 2, 1 cos a sin"-1 n 1 sin"-2 xdx. n - sin" xdx = x +…

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Q: Use a computer algebra system to evaluate theintegral. Compare the answer with the result of using…

A: To determine: The value of the integral tan5x dx using the computer algebra system and also by using…

Q: Express the integral as a limit of sums. Then evaluate the limit. | sin 11x dx

A: Solve the integration

Q: 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= to 3.459 square units…

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Q: Evaluate the integral [ ª sin(tan x) dx cos² x

A: Given- ∫sintanxcos2xdx To find- The value of the above integral. Concept Used- The above integral…

Q: Evaluate the integral. integral   sqrt tan x / sqrt sin x dx

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Q: 2. What Is the frequency of the perlodic function f() = 2 tan

A: Given, periodic function is                                    f(θ)=2tan2θ3

Q: Use an appropriate substitution and then a trigonometric substitution to evaluate the integral. 9+x…

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Q: Make a substitution to express the integrand as arational function and then evaluate the integral.

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Q: Which hyperbolic functions are increasing on their domains? A. tanh x and cosh x are increasing on…

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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: Express the integral as a limit of sums. Then evaluate,using a computer algebra system to find both…

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Q: Evaluate the integral.

A: We have to evaluate ∫tan5θ sec3θ dθ This can be written as: I=∫tan4θ sec2θ secθ tanθ dθ=∫tan2θ2sec2θ…

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A: In this question, we find the line integral for given vector function and parametric path.

Q: Verify Rolle's theorem for the function sin x f(x) = et on [0, n]. %3D

A: Given:                      f(x)=sinxex on 0,π                     f(x)=e-xsinx     The mean value…

Q: tan x sin ydydx

A: To find: ∫0π3∫0π3tanxsinydydx

Q: Express the limit as a definite integral on the given interval um 2 x; In(2 + x?) Ax, [0, 2] i = 1…

A: Given expression limn→∞∑i=1nxiln2+x2i∆x,0,2 We know that ∫abfxdx=limn→∞ fxi∆x......1Where, ∆x=b-an…

Q: evaluate using methods similar to those that apply to integral tanm x secn x.

A: Given integral  By using the identity we get

Q: 5x'/1 – x² dx

A: Given: I=∫015x31-x2dx For evaluating given integral, we substitute x=sinθ…

Q: Evaluate the integral (secle).tan co)) do

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Q: Use Simpson's Rule with ne4 to estimate Cos"xdx COSTX ☺ For ☺ an upper bound for the estimate. Hint:…

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Q: Prove that 2 arcsin (x) = arccos (1-2x2) for XE (0,1 )

A: Concept: Trignometry inverse formula: One of the key ideas in mathematics is the inverse…

Q: Example. Sind Susface area of Z- S4-X2 above ২-

A: Recall:  Surface area, A=∫∫R1+zx2+zy2dA We have, z=4-x2,  R=[0,1][0,4]

Q: Verify Rolle's theorem for: f(x) = e*(sinx - cosx) on

A: Given:

Q: To evaluate f dx, the integrand can be transformed to 1-sin?x

A: Follow the procedure given below

Q: Find Fourier sertes [o, 2] an 2) fex) f Cx) = Sin X ニ

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Q: Use integration by parts to prove the reductionformula.

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Q: Sa J (1+ In² sin x)5 “ cot x In sin x dx

A: Let the given integral be y - y = ∫cotx lnsinx1+ln2sinx5 dx           ..............(1)Let,u =…

Q: True or False: To evaluate the integral tan a sec" zdx, we save one sec z factor and use sec z = 1+…

A: Answer: TRUE

Q: Show that the functions have exactly one zero inthe given interval. r(θ) = 3 tan θ - cotθ - θ, (0,…

A: Show that the functions have exactly one zero in the given interval. r(θ) = 3 tan θ - cotθ - θ, (0,…

Q: Use the addition formulas to deriv TT 31. cos(x - sin x 2

A: Prove that cos( x  - π/2 ) = sinx Here we use general formula : cos( A - B ) = cosA×cosB + sinA×…

Q: Evaluate the integral.

A: Let the given integral be y - y = ∫sin-1x2dx            ...............(1)Let,x = sinθ…

Q: | tan° 0 sec® 0 do

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Q: What is the integral of fsin sin x dx? а. - cos cos x + C c. sin sin x + C tan r

A: Note  Your Question is wrong because their is no anti derivative of sin(sinx) so correct option is…

Q: Evaluate the integral using the indicated trigonometricsubstitution. Sketch and label the associated…

A: Consider the integral  ∫x3x2+4dx

Q: O Evamate the triple integral メ2 "Sinydy dzdx

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Q: Find the area bounded by the trigonometric curves y=sinx and 2.828 square units 1.414 square units…

A: Given that curve y=sinx and y=cosx    from x=π4 to x=5π4To find :Area bounded by the region from…

Q: 6. Is f continuous at 0? Explain your work carefully. { 2² . sin(-) + cos(-) ifz+0 | f(x) = %3D if x…

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Q: find the intergral of f(x) = sin(x) + cos(2x) on the interval [0,pi]

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Q: Write the improper integral which is represented by the following limit. 2x dx lim C-2 Show that the…

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Q: The area under one arch of y=sin(0.5x) is O 0.2 O 0.5 O 0.8 None of them

A: Given: y=sin(0.5x)

Q: Evaluate the integral. "1/3 tan (x) sec*(x) dx

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Q: Use the trapezoidal rule with n = 20 subintervals to evaluate I = -5 sin² (√0× t) dt

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Q: Differentiate each of the f cosh(x)+1 cos(r)+1 a. Y =

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Q: Make a substitution to express the integrand as arational function and then evaluate the integral.…

A: To find the integral: ∫sinxcos2x-3cosxdx Let substitute t=cosx Differentiating both sides,…