9 sin () Calculate the average of f(x) = over the interval [1, 2]. %3D (Use decimal notation. Give your answer to three decimal places.)

Q: Determine the local extrema of the function f(x)=sinx−cosx on [0,2π].

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Q: (24) Evaluate the integral: | Va sin(1 + x/2)dx.

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Q: 4.62. Evaluate the derivative of the Gamma function and see dT'(x) r'(x) = dx ' (In t)e"'dt

A: To differentiate the gamma function:         Γ(x) = ∫0∞tx-1e-tdt Integral definition of gamma…

Q: at f" si sin rdr = 2, find the average value of the sine function on the interval [0.7]. Also, find…

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Q: 4) fG) = (2x+ 1)9 %3D

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Q: Calculate the average rate of change of each of the following functions over the interval…

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Q: 6. Identify local extrema for the following use the First OR the Second Derivative f(x) = sin (x),…

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Q: a) Find the first derivative of the followings: i) f(x) = sec²x tan/x ii) f(u) = cos²(sin(1 – u)-1)…

A: We have to find out the derivative

Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x      ...(1)

Q: What is the value of this derivative at the origin? 1.4 Consider the following two functions: (i)…

A: It is given that Consider the following function

Q: Need help

A: Given function:

Q: The slope of the line normal to the graph y = 2 ln(sec x) at x = is: O-1/2 O non-existent O-2 2

A: The graph y=2lnsecx at x=π4

Q: Find the first derivative of the function below: f(x) = (cos(2a – 7))sin(z+1) %3D

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Q: х+1 3.) y = х-2

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Q: Use differentials to estimate sin(0.1). A) 0.0017 0.0099998 0.0998 D. 0.1

A: Give: To using differential s to estimate value of Sin(0.1)

Q: 7. Find the integral of the hyperbolic function below. 6 sin(x) cosh[cos(x)] dx

A: Evaluate: ∫6 sinx coshcosx dx

Q: 4. Let g be defined by the function below. SV25 – x2, x2 – 5, -4 < x < 0 0 < x < 3 g(x) = a. Find…

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Q: 5) y>10 (3v-1) (1+5w)

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Q: Let z= sin (y²– 4x). Find the rate of change of z with respect to x at the point (2, 1) with y held…

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Q: Let f(x) = sin x, g(x) = cos x, and h(x) = 2x. Find the exact value of the expression, the average…

A: we have been given f(x)=sinx, g(x)=cosx and h(x)=2x. we have to find the exact value of the…

Q: 9.) f(x) = (2x + 1)* %3D

A: The integration technique to calculate the first derivative is:∫(ax+b)n-1…

Q: 10. S(tan x – 1)²dx

A: Topic:- application of integration

Q: a) Find the first derivative of the followings: i) f (x) = sec²x tan/x ii) f (u) = cos²(sin(1 –…

A: We have to find the first derivative of given function

Q: 35. Does the graph of Sx*sin(1/x), x + 0 f(x) (o. x = 0 have a tangent line at the origin? Give…

A: Given: fx=x2sin1x,x≠00,x=0

Q: Let f(x) = sin x, g(x) = cos x, and h(x) = 2x. Find the exact value of the expression, the average…

A: Given function: fx=sinx

Q: 1. S(esin x cos x - acos 2x sin 2x)dx

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: (ii) Hence, by using Leibniz Rule for Differentiation Under the Integral Sign, compute the value of…

A: Leibniz Rule for Differentiation under integral sign:- ∂∂t∫atbtfx, tdx=∫atbt∂f∂tdx   + fbt, t∂bt∂t-…

Q: Let h (x) = x sin . 1. Find the x-values where h has horizontal tangent lines in the interval 0, 27.…

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Q: 8. Using any work found in Question 7, determine the 3x (x? - 5)° dx a.

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Q: Q2]Using Simpsons1/3 rule for evaluation of sinh(e-*) dx use n = 4 andwork to 5 decimal place?

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Q: 10. Consider the function f(x, y) = 4 + x* + 3y* a. Show that the Second Derivative Test is…

A: (a) Calculate the value for second partial derivatives w.r.t x and y.…

Q: 3:Use Gamma & Beta properties to evaluate : f (In x)³ dx

A: The gamma function is Γ(z)=∫0∞e-ttz-1dṭ The Gamma function is a non-integer generalization of the…

Q: Estimate cos(x²)dx by using a right-hand sum and 4 subintervals. |cos(x²)

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Q: Find the average rate of change (AROC) of the following functions over the interval [60 ≤x≤180] y =…

A: using , average rate of change…

Q: The first derivative of the function h is given by h'(x) = tan(0.1x- x) for -n < x < R. On what…

A: Solution Given h'(x)=tan(0.1x3-x) for -π&lt;x&lt;π.we need to find on what intervals is h…

Q: find the average rate of change of the function overthe given interval or intervals. g(t) = 2 + cos…

A: gt=2+cost,  0, π

Q: sinx f(x) = on [0, 2n] cos x-V2

A: Given :         f(x) = sin xcos x - 2 on 0, 2π   To determine the extrema of the above function…

Q: (0)3-3x+2 sinh' (In x) cosh (In x) (E) sin(2x)dx dx N

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Q: = 1. Use a local linear approximation of the function f(x) = ln(x + sinh(x) + cosh(x)) at some point…

A: Since the required point is 0.001 near to 0, so we approximate linearly about x=0, also at this…

Q: Consider the function  f(x) such that (a)  f(1)=1/ln^2 and (b) the tangent line at  (x,f(x))  has…

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Q: Find the average rate of change of the function over the given interval. Compare this average rate…

A: Average rate of change: Average rate of change of any function f(x) of [a, b] is, fave=fb-fab-a…

Q: 3 5.) y = ; x+5

A: Given:- y = 3/(x+5) y = 3(x+5)-1 Using Formula : [f(x)g(x)]' = f(x)g(x)' + g(x)f(x)' Now, y' =…

Q: Find the relative extrema of f(x) = 1/2x − sin x in the interval (0, 2pie ).

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

Q: 1.) Find the area under the curve y = x3 + 3x2 and the axis between x = 1 and x = 3.

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Q: In (sinh x ), + tanh x j + 1-x k )dx 1- sinx

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Q: (29) Evaluate the integral: r/3 csc? xdx. (30) Find the derivative of the integral function: g(x)…

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Q: Let -sin (y-4x) Find the rate of change of z with respect to y at the point (2, 1) with x held…

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Q: 1.) f(x) = (2x + 1)(3x – 2)

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Q: 21. Find y' using implicit differentiation. a) In (xy + x + y) = 2 b) In (sin xy) = xy

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