Find f '(a). 3t + 9 f(t) : t + 4 %3D Step 1 To find f'(a), we will use the formula f '(a) = lim t) – f(a) t - a Since f(t) 3t + 9 we have %3D t + 4 3t +9 t + 4 t - a За + 9 f '(a) = lim a + 4 . Putting the fractions in the numerator over a common denominator and simplifying, we have 3t + 9 За + 9 (3t + - (3a + 9)(t + 4) %3D t + 4 a + 4 (t + 4)(a + 4) 3ta + 9a + 12t + 36 - 3at - 9t - 12a - 36 (t + 4)(a + 4) %3D (t + 4)(a + 4)

Q: A cat is falling from a branch. Its height t seconds after it fell is given by the function h(t) =…

A: We have given height  ht=-16t2+5 To get for what height cat was falling  Put t=0 h0=0+5 h0=5 height…

Q: I need help with the rules for finding the difference quotient. for example. f(x)= 1/x^2

A: To evaluate the difference quotient for the given function

Q: I did that, factored x^2 + x +6 and got x=-2 and x=3 so the vertical asymptotes should be 2 and -3,…

A: You have done the wrong factorization the factor of x^2 + x +6 is not -2,3 . When we factorize then…

Q: Q(x)=5x^2-19x-4/2x^2-7x-4 Find the vertical, horizontal, and oblique asymptotes?

A: We have given  Q(x)= (5x2-19x-4)/(2x2-7x-4)

Q: 5 Lim 34 +7 y?_2

A:

Q: limx→0 (1−cos(5x))/(1−cos(9x))

A: Used L'Hospital rule

Q: Determine the equation of the oblique asymptote of the equation f(x)=2x^2-9x+10/2x-1

A:

Q: ƒ (x) = − ½-|x| − 14x^8 +7   is this a function if so how and why

A:

Q: The graph in the picture below shows the function f(x) = 2^x+2 a) on the same coordinated grid…

A: The equation of g(x) = 2x+2 -2And the graph is given belowExplanation:Concept :  Scaling:−when you…

Q: f(x) = x² + 3x + 4 f(x + h) – f(x) First, find h |(x^2+2hx+h^2+3x+3h+4)/h Preview Next, simplify the…

A:

Q: If f(x)=x^2 and g(x) is the graph of f(x) shifted to the right 3 units, stretched vertically by a…

A: When f(x) shifts 3 units right then it becomes f(x-3)

Q: f(z +h)-f(z)

A:

Q: (2x + 4) sec2(x2 + 4x)

A: ∫(2x+4)sec2(x2+4x)dx Formula ∫sec2x dx=tan(x)+C

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.