4. Differentiate the following. Simplify your answers. っ 7m)²/3r 116 エコノー

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A: limx→-1(3x-5) = limx→-13x - limx→-15  [ lim(a - b) = lim a - lim b ]                         = 3…

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A: answer is in next step

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Q: Q3/ Evaluate four of the following integrals. ( x³+1 sinx cosx dx b. f*+¹ dx c a. S √1+cos2x x²

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A: This question is based on modulus of complex number.

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A: We need to find the polar equation which is symmetric only with respect to the polar axis (x-axis).

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Q: Use symbolic notation and fractions where needed.) a= b = C = d =

A: Topic:- calculus

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A: Given :w=xz+yzx=cos2t    and y=sin2t   z=1t

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A: To find the laplace transform of the given function.

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A: The given function is: y=9x+8   As we know that; The Sum/Difference Rule: f±g'=f'±g' The Power Rule:…

Q: Directions: Using Fundamental Theorem of Calculus (FTOC), compute the following definite integrals.

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A: If f(-x)=-f(x), then f(x) is called as Odd Function.

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Q: 1 +x² √x (+/- + x² Given f(x)=x√x + x and g(x) - = f(x) (exe-1-x-3/4+) (² + x² g(x) √x)² 1 ° = [e…

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Q: 5. How is -28 can be express as rational number with numerated the number 4? 84

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Q: 3. Let there be some a, b ER such that f(a)f'(a) = f(b) f'(b) + 1. Show that f f(x)f"(x)dx ≤ 1.

A: This is a problem related to integration. Based on the general formula and concept we will prove the…

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A: We can find the solution as below.

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A: We have to find the area.

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A: We can find the value of x as below.

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A: The limit definition of derivative of a function at x=a is given by  f'(a)=limx→af(x)-f(a)x-a. For a…

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A: We have to find out derivative