Calculate (1/2 (2 (2t - 1)e³t dt.

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A: To solve the problem of differentiability by seeing the graphs of the function.

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Q: evaluate the integral: Given that [₁² f(x) dx = 3, [²9(x) dx = 2, f(x) — 3g(x) 2 [²³ F (² dx.

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A: Given; Lima-1[1/(a-5) -1/6]/(a-1).

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A: Please see the below picture for detailed solution.

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Q: a. J(a) Problem 9: Draw the derivative of the function -10 11 F3 -5 10 10 0 -5 -10 V F5 5 F6 10…

A: We have to draw the graph of f(x) derivative by see it's original graph f(x).

Q: 8. a 10, b= 11, c= 12

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A: The answer is given below:

Q: g(t)=t-3 h(t)=-3t³+6t Find g(1) +h(1) h(t)=t+5 g(t)=3t-5 Find (h. g)(5)

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A: Given Expression: y=1x3-2ln(x)+5x4        .........(1) y=ex-4x-3(2+x     .........(2) y=2x2-4x+17x+4…

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A: We want to find unit tangent vector, unit normal vector and the curvature.

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A: Given that  r→(t)=cos2t,sin2t,t

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Q: Let f(x) = −sin(x)and g(x) = cos(x). Find [f(x) g(x)]. dx d -[ƒ(x) • g(x)] = sin²(x) - cos²(x) dx d…

A: This question can be solved using product rule of differentiation.

Q: 1. (x+y)y' = x - y

A: Note as per guidelines we support one question in one request.kindly repost next question in next…

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A: The standard form of line equation is  y=mx+c  where  m= slope=6/5 c= y intercept=6

Q: Find the domain and range of function and show your solution thanks.

A: Domain of a function y=f(x) is the set of values of x for which y is defined.   Range of a function…

Q: 4 -3 42 -1 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 1 12 Identify the function whose graph appears above as f(…

A: We can solve this as follows:

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Q: et f(x) = 2x³ 4x² + x - 1 23 a) Use division to rewrite the function as individual terms with…

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Q: 1. Differentiate y = √e(72²-2) (a) by using the chain rule directly with functions f(x) = VI and…

A: Given, y=e7x2-23

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A: Note: Hooke's law: F= kS Where F is force  k- elastic constant S-strain   Work formula: W= F.S…

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A: we need to find the equation of tangent line.

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Q: Given the graph of y = f(x) shown below, what is the graph of y = f(x - 4) + 3? -7-6-5 |||||| 3 -I…

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Q: Find the general solution of each of the following. 1. tan x dx + y cos² x dy = 0

A: The given differential equation is; tanx dx + ycos2x dy=0. Repost the next questions.

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A: Here we have to solve the differential equation.

Q: 495745947949979437 x 7826736386487342622 - 1000000 x 634634662354 + 8766348764410939824383658 x 8483…

A: We can solve this as follows:

Q: Consider the system 0 [9 -4a-1 -b-3 1-8a -26-6 a. Given that b-3, for which value of the parameter a…

A: Here we have to use the concept of system of linear equations.  I have appended the formula used in…

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A: Given: The graph of the function f(x) is given. To find: The graph of the derivative function:…

Q: Find the slope of the normal line to the curve f(x) = √x+1 at (3,2). B-1/4 1/4 ***

A: Topic- slope of the normal line for function y=f(x) ,slope of the normal line to f(x) at x=c is…

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Q: lim (g4) co (y¹) (²2) y→0 24

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Q: Let f(x) = x² + 9, g(x) = x − 8, and h(x) = √√x. Find the given compositions. Expand and simplify…

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Q: For what values of a and b is the line -15x + y = b tangent to the curve y = ax5 when x = 1 ? a = |…

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