Find the domain of each function. (Enter your answers in interval notation.) (a) g(t) = sin(e-t) (b) g(t) = 1 – 2t

Q: have any horizontaltangents in the interval 0 … x … 2p? If so, where? If not, why not?Visualize your…

A: The given curve is y=2x+sinx Here, the curve has a horizontal tangent that means, the tangent is…

Q: Find the distance between the two values of x at which the function is discontinuous. x²- 3x + 2 2.…

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Q: Find all values of x for which f(x) = e?*(x² – 12) has horizontal tangent lines. %3D

A: Horizontal tangent meaning slope of those tangent are zero . Take the derivative and equate to zero…

Q: Find an equation of the line tangent to the graph of f at the given point. f1x2 = sin-1 12, p>62 4

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Q: -x/18 flx)= xe [-2.6

A: It is absolute maximum and minimum problem.

Q: Q2// A – If y = tan-1(-1), find the value of y without use Calculator. B- Find the Domain, Range and…

A: To find Value of y if y=tan-11And  to graph y=2cos(x-π3)

Q: Consider the function f(x) =3 on the interval [1,5]. A graph of the function appears to the left.…

A: SOLUTION-

Q: Find all values of x for which the tangent line of f(x) = /x² + 18x+96 is horizontal. A 0,-9 B 0,9 С…

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Q: a. Determine the point (a, la)) for which f'(a) = a, given that Ax) = -x + 3x-7. b. Write the…

A: For (a), Given: We need to find the point a for which f'(a)=a. Here, f'(x)=-2x+3. So,…

Q: Find an equation of the tangent line to the graph of the function at the given point. g(x) = ex5 −…

A: Given equation of curve is Differentiating with respect to x, we get We know that slope of tangent…

Q: Find the absolute extrema of the function on the closed interval.

A: Consider the function g(x)=sec x on the interval -π6, π3 To find the absolute extrema of the…

Q: The function f is shown below. If g is the function defined by g(x) = | f(t)dt, write the equation…

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Q: Find an equation for the line tangent to the graph of f(x) = -6xe" at the point (a, f(a)) for a = 2.

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Q: Find the domain and range of the function, f(x)= sec x+1

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Q: - 3x + 1, x S 4 Find the value k , if the function ƒ (x) = is continuous at x = 4. -kx + 1, x > 4

A: We will find the value of k as following.

Q: The amplitude and period of the function y=4-a/2cos(bx/3-π) are 3 and 4π, respectively. Find |a|+b

A: Given amplitude=3 period =4π

Q: Find an equation for the line tangent to the graph of f(x)=−7xe^x at the point (a,f(a)) for a=2.

A: Given:

Q: Find reference point of t when t = -5 pi/4

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Q: Which of the following is an equation of the line tangent to the graph of f(x)=3x^2+1 at the point…

A: Please refer the attached image for complete solution.

Q: dr a) -sin³ x b) sin² x Q7. Find the range of the function y= a) x>0 b) x 3

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Q: State the intervals where the graph of y = sec(r),-2n <I< 27, is decreasing.

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Q: For what values of æ does the function f (x) = 12x – æ³ have a horizontal tangent line? Select all…

A: The given function is fx=12x-x3

Q: Use a calculator to graph f(x). Use the graph to solve f(x) > 0. (Ent F(x) = +2 %3D f(x) > 0 when x…

A: Graph of function

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = Inx?;…

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Q: find and sketch the domain for each function ƒ(x, y) = ln (x2 + y2 - 4)

A: To Determine: find and sketch the domain for each function ƒ(x, y) = ln (x2 + y2 - 4) Given: we have…

Q: For what value(s) of x does the function f(x)= 4x3-x2-2x+5 have a horizontal tangent line?  a.) x=…

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Q: Find the equation of the tangent line to the graph of y =f(x) at the point where x=-3 if f(-3) = 2…

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Q: Q1. Consider the function f(r) = a2 +a - 4. b) Find the equation of the tangent line to the graph of…

A: To find: The equation of tangent line to the graph of fx=x2+x-4 at x=-1 and show it on the graph.…

Q: Use the First Derivative Test to find the x-value(s) at which the function f(a) = + 4x? 2 9x? + 4…

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Q: Find the value of 'a' for which the tangent to th ƒ(x) = (a + 2) x³ − 3ax² + 9ax - 1 never makes an…

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Q: Q3: Find The Domain of the Function. Inx|- y = sin

A: Explanation of the solution is given below...

Q: Q 8/ Find all points on the graph of f(x)= (x-3)(x-2) at which the -1 tangent line is horizontal.…

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

Q: At what points the given functions are discontinuous? 1 y = - X - 2 (i) 3x

A: To find: The point where the function is discontinuous. Given: The function is y=1x-2-3x. Concept…

Q: 2:- Sketch the following functions (in steps), then find their domains. a) y= b) y= tan

A: We have to sketch the functions and also find the domain. a). y=1sin-1xb). y=1tan-1x

Q: Use the equation below to find the tangent line to the graph of the function f(x) = 6 − 2x^2 at the…

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Q: Q6: Find the absolute maxima and absolute minima For the function f(x) =sinx 0 < x < 2n

A: To find the absolute maxima and absolute minima, first, we have to find all the critical points of…

Q: 2x-5 Find the equation of the tangent line to the graph of f(x) = at the point at which x+1 x = 0.

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Q: x+1 At what points is the function y = continuous? x2 - 6x + 5

A: To solve this problem we will use the concept of continuity of rational function.

Q: Find the equation of the tangent line at the point (a,f(a)). Sketch the graph and the tangent line…

A: To find the equation of the tangent line at the point (a,f(a)).

Q: On the graph of f ( x ) = sec ( x ) and the interval ( -2π, 0 ], for what value(s) of x does f ( x )…

A: f(x) = 1 on, (-2π, 0] Implies, sec(x) = 1 on (-2π, 0] i.e. x = 0 on (-2π, 0] So, x = 0  The graph of…

Q: x+4 VI. At what points, if any, is the function(x) = x2-x-12 discontinuous?

A: We have to find the points

Q: Find f'(x) and find the equation of the line tangent to the graph of f at x= f(x) (2 + 3x)(6-5x)…

A: Given:

Q: On what interval(s) is the function -9x3 g(x) = e both decreasing and concave down?

A: The interval in which the given function g(x) is both increasing and concave down must satisfy the…

Q: What is the period of the function? Ay 2 3t 4 5 6 7 8 9 0n -1 -2 -3 -5 5432

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Q: Is this function harmonic? 2x + y³ – 3x?y a. Yes O b. No O c.Not at all O d. all of the above

A: coreect option is a. YES

Q: 3. Given the function g(x) = x - 2x2 + x, find the interval(s) when g is concave up and decreasing…

A: We have given a function g(x).  We have to find the interval where g is concave up and decreasing at…

Q: 1 + y =

A: To solve the following problem, we use the concept of seperation of variable, then integrate both…

Q: On the graph of f(x)=sinx and the interval [−2π,0), for what value(s) of x does the graph cross the…

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Q: On the graph of f(x) = = 1? Choose all answers that apply. = cscx and the interval [-2n, 0), for…

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Q: (a) If F(x) = 5x/(1 + x²), find F'(2) and use it to find an equation of the tangent line to the…

A: Consider the given function as y=5x1+x2