Let  f(x)=sin(ln|x|). Justify whether limx→0f(x) exists. If it exists, enter the appropriate value. If it does not exist, select the behavior of the function near x=0 that causes the non-existence.  You may also choose NA if the provided choices do not fit your conclusion.  A.   NA B.   -1 C.   Oscillatory D.   1 E.   Finite jump F.   removable discontinuity G.   0 H.   Unbounded

Q: 1. lim f(x) = -1 and f(1)DNE 2. lim f(x) = 1 and f(0) = -3 3. lim f(x) = -2, lim f(x) = 2 and f(2) =…

A: we will find type of graph around given value of x to draw graph

Q: 2. Sketch a graph of a quartic polynomial function y = fx) such that: € fu) > 0 when - 2 1

A: In the given question we have to draw the graph of a quadretic polynomial s.t f(x)>0 when…

Q: x-9 Q.4 Let f (x)={ x+3 ,x#3 Find the value of k for which limf(x)=f(3). k,x 3

A: Given

Q: Shown below are six statements about functions. Match each statement to one of the functions shown…

A:

Q: If p is true, q is true, and r is true, find the truth value of the statement. (~pv-q) v-r Select…

A:

Q: Suppose that ƒ′(x)<= 1 for 1<= x<= 4. Show that ƒ(4) - ƒ(1)<=3.

A: Show that:

Q: Q8. We shall formally show that if two functions f and q are both differentiable at c, then we have…

A:

Q: Cite 1 example of real-life application of midline theorem.

A: Midline theorem:  In the triangle, the line segment that joins the midpoints of two sides of a…

Q: 2. Assume all given functions are continuous. If lim (f(x) - g(x)) = 10 and ƒ(5) = -8 x → 5 Find g…

A: The objective of this question is to find the value of g(5) given that the limit as x approaches 5…

Q: 1. Let g(x) = 3 %3D I-2 a. Compute lim, g(x); - L X- 2 b. Give equations of any horizontal and…

A: The objective of the question is determine the limit of the given function and find its asymptotes.

Q: Evaluate the following: -1 x-1(x+1) xả-5x-20 x-5 x²-4x-5' x-5 lim x-5x²-10x+25² i. lim ii. lim iii.

A: note :Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: Iff and g are continuous functions with ƒ(7) = 10 and limx→7 [2f(x) — g(x)] = 7, find g(7).

A:

Q: If V5 – 2x? < f(x) < V5 – x? for -1 <x < 1, find lim,-o f(x).

A: Given  5-2x2 ≤ f(x) ≤ 5-x2 for  -1≤x≤1.

Q: s(x) = - V – 1 100 10! 102 103 F (x) 104 105 106 f (x) lim

A:

Q: 2. Assume all given functions are continuous. If lim (ƒ(x) – g(x)) = 10 and ƒ(5) = −8 x → 5 Find…

A: The objective of the question is to find the value of g(5) given that the limit as x approaches 5 of…

Q: 2. Assume all given functions are continuous. If lim (f(x) - g(x)) = 10 and ƒ(5) = -8 x → 5 Find g…

A: The objective of this question is to find the value of g(5) given that the limit as x approaches 5…

Q: If f(x) = (3x – 2)10 , then f(1 + h) – f(1) lim h→0 h О 15 O 5 o 7.5 O 10 O 30 O 20

A:

Q: f(r+h)-f(x) 1. Use the definition f (x) = lim to find the first derivative for the function h0 h…

A:

Q: Find the value of lim f(x), if x→7+ S8x + 2 x 7 f(æ) = 45 9. O 16 O 87 O 57

A:

Q: 2. Assume all given functions are continuous. If lim (f(x) - g(x)) = 10 and ƒ(5) = -8 x → 5 Find g…

A: The objective of this question is to find the value of g(5) given that the limit as x approaches 5…

Q: Suppose that f(x) = Ax² + Bæ. Find the values of the constants A and B if f(2) = -4 and %3D…

A: We have to use definition of limits.

Q: The following function may be viewed as a composite function h(x) = f(g(x)). Find f(x) and g(x).…

A:

Q: 2) a) Recall that the definition of the derivative of a function f at a point a is given by f(a + h)…

A:

Q: If x= 1.3 + 3.6 1.3.5 3.6.9 + 1.3.5.7 3.6.9.12 + then P.T. 9₂²°²+24x=11 ,

A:

Q: (3x-7 x21 lim f(x) = 19. (x)= r+4 x<1 %3D

A: 19) The given function is fx=3x-7x≥1x2+4x&lt;1 To find: limx→1-fx

Q: All work must be shown to receive full credit for a correct solution. Partial credit may be given if…

A: A detailed solution is given below.

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.