I need help with this problem. Please answer and explain! (Ignore selected answer)
1 answer:
Answer:
g'(0) = 1
Step-by-step explanation:
The derivative of a function g at a number a, denoted by g'(a), is given by the definition of the derivative:
In the definition of the derivative, "h" can be understood to be the horizontal change in the function with respect to a number <em>a</em>.
So g'(0) is
The variable in the limit is bound; without any other variables around, we can change the variable name to another reasonable variable name and it will still be the same. Hence we can change h to x and it will be equivalent:
thus the given limit implies g'(0) = 1.
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Answer:
<h2><em>(3,6)</em></h2>Step-by-step explanation:
Given two coordinates (x₁,x₂) and (y₁,y₂), their midpoint (w,y) is expressed as:
M(X,Y) =
From the question, we are given the midpoint (X,Y) to be (2,2) and one endpoint as (1, -2) and we are to find the other end point expressed as (w,y). From the coordinates given, i can be seen that X = 2, Y =2, x₁ = 1 and y₁ = -2
Substituting the given end points into the given formula to get the other end points, we will have;
Similarly;
<em>Hence the other endpoint (w, y) is (3,6)</em>
Recall:
The tan of the measure of an angle is the ratio of the opposite side to the adjacent side to that angle, that is :
.
Since this ratio is 3/y, we denote the opposite side, and adjacent side respectively by 3 and y.
(Technically we should write 3t and yt, but we try our luck as we see y in the second ratio too!)
Similarly,
.
The adjacent side is already denoted by y, so we denote the length of the hypotenuse by z.
Now the sides of the right triangle are complete.
Answer: A
The tan of the measure of an angle is the ratio of the opposite side to the adjacent side to that angle, that is :
Since this ratio is 3/y, we denote the opposite side, and adjacent side respectively by 3 and y.
(Technically we should write 3t and yt, but we try our luck as we see y in the second ratio too!)
Similarly,
The adjacent side is already denoted by y, so we denote the length of the hypotenuse by z.
Now the sides of the right triangle are complete.
Answer: A
Answer:
Step-by-step explanation:
Let's start with the original function.
We can immediately fill in the amplitude 'a' and period 'T' , as the question defines these for us, and provides values for 'a' and 'T', 4 and 4 respectively.
Now we only have phase shift and vertical shift to do. Vertical shift is very easy, you can just add it to the end of the right side of the expression. A positive value will shift the graph up, while a negative value will move shift the graph down. We have '-2' as our value for vertical shift, so we can add that on as so:
Now phase shift the most complicated of the transformations. Basically, it is just movement left or right. A negative phase shift moves the graph right, a positive phase shift moves the graph left (I know, confusing!). Phase shift applies directly to the x variable, or in this case the t variable. To achieve a -4/3 pi phase shift, we need to input +4/3 pi into the function, because of the aforementioned negative positive rule. Here is what the function looks like with the correct phase shift:
This function has vertical shift -2, phase shift -4/3 , amplitude 4, and period 4
.
Desmos.com/calculator is a great tool for learning about how various parts of an equation affect the graph of the function, If you want you can input each step of this problem into desmos and watch the graph change to match the criteria.