y = С₁e-¹/² + С₂e-4t

Q: What else do you observe? Concept Check: Evaluate the following integrals: e3x dx 1-2e3x 2.5 1²…

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Q: 22) The given equ" of the circle (x+12) ² + (y + 5) ² = 169 Here centre of the circle ins (-12,-5)…

A: The following is the digital format of the given text.

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A: see below the answer and calculation

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A:

Q: Solve the equation: 5-2 = 32+1

A: See this solution in below.

Q: x + 3y s 18 2x + yΣ 14 x Σ Ο Υ Σ Ο

A: See this solution in below.

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A: Given solution :

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A:

Q: arcsin = ab²x² - √a² - y²; Find y. I

A: Recall: y'=dydx

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A:

Q: Evaluate the following integral using integration by parts. Jxsin 8x dx 6x OA. x cos 6x + cos 6x COS…

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Q: 2) Solve 2y" +5y' = 10, where y(0) = 1, y'(0) = 0. (hint: use integrating factor)

A: Given :solve 2y" + 5y' = 10 , where y(0) =1, y'(0) = 0

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Q: Combine into a single logarithm log3 - 4 log; y + 2 logą z − 2 O 10g3 O log3 2yª O 10%3 gyt 2½ O…

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Q: Find the derivative of: - R(t) = (sin² (3t+1), ln(t² − 1), ²) +1

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Q: . Evaluate the for parametric equations x = 3t² - 6t and dx = 3t³ + 3t with respect to the…

A: Given query is to find the Indicated derivative.

Q: π/4 de Evaluate the integral √ (secx + cos x)² dx LENT O blen

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Q: @fő)= 5. Find the hypercritical values of the function. f(x) = + x ²² 36x² - 12x² hev's @concup=…

A: Hyper critical values:- those points where the function second derivative is either zero or…

Q: Evaluate the integral 10 10 sin(x) cos(x) Note: Use an upper-case "C" for the constant of…

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A: Please see the answer.

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A:

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A: Equation of quadratic function having vertex (-4,-1)

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Q: eln9

A: Given:- eln9

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A: To find the velocity and acceleration vectors for the given position function.

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A: GIven Cost function:- Cx=x32000-x250+50x+20,000

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A: Topic -Application of derivatives We are given a cardboard of 20 inch by 32 inch and we need to find…

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Q: Evaluate the following integral using partial fraction decomposition. S 12 (x-4)(x+8) 12 (x-4)(x+8)…

A: The given integral ∫12x-4x+8dx We have to find the integral using partial fraction.

Q: The half-life cesium-137 is 30 years. Suppose we have a 100 mg sample. a) Find the mass that remains…

A: The equation for decay is:Pt=P0ektwhere t=time in years, P0 is the initial mass.

Q: What else do you observe? Concept Check: Evaluate the following integrals: fe3xe 1. -5x dx

A:

Q: In the equation for the Laplace transform of a periodic function, L {f(t)} = ₁- ²- Sőe¯st f(t) dt,…

A: The Laplace transform of a periodic function:Lft=11-e-sT∫0Te-stft ft

Q: evaluate the iterated integral

A: Fubini’s Theorem If f(x,y) is continuous on R=[a,b]×[c,d] then, ∫∫R…

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A: Let's find given diffential equation is separable or not.

Q: Solve iii. Integral x^2 square root x+1 dx. Evaluate the given integral be selecting and using…

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Q: Problem 1 Given a first-order differential equation: √1 + x² dy - ydx = 0 a) What is the best…

A: We have to find the general solution and the particular solution of the given first order…

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Q: Find the Maximum value of the function f(x,y)=x^2−y^2−2y on the curve x^2+y^2=4.

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Q: 20. Evaluate the limit or show that the limit does not exist. Show proper work. sin y cos y ye (a)…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 1. sin(In 41x) X dx

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. || y=…

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Q: Graph Oct 21, 12:08:04 AM A particle moves along the x-axis so that at time t≥ 0 its position is…

A: Given query is to find the total distance traveled by the partical.

Q: 3. Let f(t) = t(1 - 2t). a) Find the average rate of change of f(t) with respect to t as t changes…

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Q: By using the definition of the derivative, one can sin(x) - 1 x-x/2 2x - R Identify the correct…

A: