Question 8 Let f(x) = | x-, x <1 2x+3, x21 Compute f'(1)

Q: -х- 2, х<-1 -1, f(x) =. -1sx< 0 at x = -1, 1, 0 sin(2tX), 0<x<1 X, 1s x

A:

Q: sin(x) + 2 x4 +1 5. Determine if the integral dx converges or diverges.

A: Cauchy integral test : For an&gt;0,let ∑n=λ∞an is a series of positive  terms. Then ∑n=λ∞an is…

Q: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

A:

Q: 4. Find (f-1)'(1) if f(x)=x' +8x+sin(3.x) а. Find (f-1)'(2) if f(x)= Vx' +x +xr+1 b.

A: To find the derivative of the inverse of a function

Q: Question 4 Find the derivative(f (x)) of f(x) =cos/x -/sinx a. -sin/x Cox " (x) = 2/x 2/sinx CSX…

A: By using derivative formula

Q: ) = 5 + 4 sin(x). If f(0) = 3 and f' (0) = 4, what is f(x)? Consider the function f(x) whose second…

A: Given:

Q: Find the maximum and minimum valucs of f(x) = sin x + cos x on (0, 2n].

A: Given function:                      f(x) = sin x + cos x,   x∈[0, 2π] Use the second derivative…

Q: | Example 8.12. Use the Trapezoidal rule to estimate the integral exª dx taking the number 10…

A:

Q: Show that f(x) = sin x (1 + cos x) is maximum when x = Hence find its maximum value.

A:

Q: Question 5 (1 point) The derivative of y tanh(In x) is -4x Oy = x²+1 -sech? (In x) Oy = 4 Oy =…

A: The solution is given below in the next step:

Q: Question 2 Consider a function f with domain {x|x # 0} and the following derivatives: f'(x) = bx=1…

A:

Q: Question 8 Find the derivative -[f (x)] dx Anmospace support = 3 In (In (x²-3x + 5)²) 3(2x - 3)…

A:

Q: QUESTION 2 Let f(x) be a function with second derivative of f"(x) =(x+8)(7x –11)(x – 13). Determine…

A:

Q: Find the absolute extrema of the function on the closed interval.                    f(x) = sin 2x,…

A: Approach: Without wasting any time, take the derivative of the original function. Find critical…

Q: •tanx √1+1² 0 1+e' sec ³x 1+etanx If f(x) = A B C D -dt, then f'(x) equals 1+tan²x 1+e' tan.x In…

A: Solved below

Q: 1+sin 2 x 1) Find the derivative of f(x) %3D 2 cos3 x

A: The given function is                                    y=f(x)=1+sin2x2cos3x…

Q: Question 5 Find the derivative [f(x)]; f (x) = 3 ln (In (x²-3x + 5)²). O3(2x-3) ²-3x+5 3(2x-3)…

A:

Q: Question 1. A critical point of the function g(x, y) = ey + 3x²y-y is (0,0). Use the Second…

A: Given g(x,y)=exy+3x2y-y. The critical point is 0,0.

Q: QUESTION 2 Using Mean Value Theorem, Prove that if two differentiable functions f, g agree on…

A: Prove that if two differentiable functions f, g agree on their first derivatives, that is, f'=g'…

Q: Question 1. A critical point of the function g(x, y) = ex y + 3x²y-y is (0,0). Use the Second…

A: Explained below

Q: 1. If tan-1 x x 1’ f(x) = Then S(x) dx =?

A: This question is related to definite integration, We will solve it using given information.

Q: estion 9 Find the derivative of f(z) = 3z13 - 4+1. IDo? la sin (a) f' (x) =}

A:

Q: Find (f-1)'(a). f(x) = 2x3 + 5 sin x + 3 cos x, a = 3 %3D (F-1)'(a) = %3D

A:

Q: EXAMPLE 2 Find the derivative of the function below. g(x) = 3 + t2 dt SOLUTION Since f(t) 3 + t2 is…

A: To find the derivative of the function

Q: f (x) = cos(x) f(x) = tan(sin(x)) g(x) = In(2x2 + 4x + 3)

A:

Q: 4.9. Show that if f has a bounded derivative on [a, b], then f is of bounded variation.

A:

Q: 7. Suppose the equation əz ar is a differentiable function of r and y implicitly defined by 2³ = y²…

A:

Q: ,x € (0, 2] ,a = 0 f(x) = sinx then f (x) dx = 1 3 2.

A:

Q: Question 33 1 Point Let f and g be continuous on the closed interval [0, 5]. Suppose that / f(x)dx =…

A:

Q: QUESTION 3 a) Evaluate the integral tanh (2x)sech (2x)dx.

A:

Q: Limit -1 to 1 integral (1-1/2 x) dx

A: Given:        ∫-111 - 12x dx   To find the value of ∫-111 - 12x dx   Formula:          ∫xn dx = xn…

Q: (In 3) - 3" + sinh z - find a Lets compute a derivative in reverse! Given the function S(2) function…

A: Solve by integration

Q: Differentiate the function:  k(x) = 4 ln (x) + 2 cos x + x^2 k'(x) =

A: k(x)=4ln(x)+2cosx+x2Differentiate with respect to xk'(x)=(4×1x)+2-sinx+2xk'(x)=4x-2sinx+2x

Q: If F(x) is a differentiable function with derivative F'(x)= Enx"-1 and F(0)=0, then F n=2 x2-x O 1-x…

A: Introduction: For a differentiable function fx, if f'x is given, then integrating both sides, fx can…

Q: 3. If f(-1) = 3, f'(-1) = 5, g(-1) = -1, gʻ(-1) = 2, let h(x) = f(x) g(x). Find an equation for the…

A: given: f(-1)=3, f'(-1)=5, g(-1)=-1 and g'(-1)=2 h(x)=f(x)g(x). we have to find the equation of the…

Q: Question 1 Find a classify the critical points of f(x)=-, using the two methods we learned in class:…

A: The given function is :f(x)=x55-x33 To find: Critical points of f, and  we need to classify them…

Q: Question 1 Apply the First Derivative Test to find the minimum value of f(x)=(2x^+2)/x² . Keep 4…

A: The given problem is to find the minimum value of the given function using the first derivative…

Q: 4. Find the absolute maximum and absolute minimum of the function f(x) = 3 sin(x) cos(x) over the…

A:

Q: Question 3 Consider a differentiable function g with domain [0, 0). Given that g'(x) = a e" and…

A: If g'' is negative then x is point of maxima if g'' is positive then x is point of minima

Q: Example3: a) Find the derivative of f(x.r.:)= r - -: : at P(1.1.0) in the direction of 1= 2i-3j-6k.

A:

Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2). O…

A:

Q: At which points does f(x) = 2 sin x - cos 2x have an absolute maximum value and what is the maximum…

A:

Q: 1. Find the point(s) if any where f has a horizontal tangent line. у %3D УЗх + 2 cos x 0<x < 2п

A:

Q: Module 7: Participation Activity #6 Calculate the derivative d In (t)dt dx using Part 2 of the…

A: Let the given derivative is,

Q: 268 CHAPTER 4. APPLICATIONS OF THE DERIVATIVE 38. f(x) = x In x- 2x + 3 on (0, ) 67. f(x) 39.…

A:

Q: Question 1. A critical point of the function g(x, y) = exy + 3x2y-y is (0,0). Use the Second…

A:

Q: 3 Find the maximum and minimum values for f(x) = - 4-(/2 cos x - V2 sin x)

A: Topic = Functions Maximum value of f(x)=1.5 Minimum value of f(x)=0.5

Q: Definite integrals Evaluate the following definite integrals. Use Theorem 7.7 to express your answer…

A: Evaluate: ∫-22dtt2-9

Q: How many integers are there in the domain of the function f(x) = ln (x² – x – 12) + v25 – x² +…

A: The domain of a function is the set of input or argument values for which the function is real and…