. Use the sandwich theorem sin x (a) lim Vx 400

Q: The value of the limit lim is x-0 sin x а) 0 b) 1 1 c) d) ∞

A: Given options are wrong.  Limit will be e^(1/6).

Q: e) sec mx – 1 lim

A:

Q: Use the graphs of f and g and their tangent lines at (2, 0) to find lim x) x-2 g(x) y = 1.4(x – 2) y…

A: NOTE: Refresh your page if you can't see any equations. . for the graph f, the equation of the…

Q: evaluate using Theorem 2 as necessary.

A:

Q: The value of the limit lim a) 0 b) 1 c) d) ∞ 1 X x-0 sin x sin x 6 is

A:

Q: (a) Find the exact value of the overshoot lim E 1/1- dx/x?

A: Given limn→∞∑j=1n1/j2-∫1πdxx2

Q: Evaluate using Theorem as necessary.

A: Given limit: limt→0 t3+9sin tt We can write the above limit as limt→0 t3+9sin tt=limt→0 t3+9×limt→0…

Q: Find the limit of the following lim    ln(cos(x)) x→(pi/2)-

A: Consider the given limit.

Q: 7 sin(T2) In (zº) q(z) = %3D What is lim q(x)? ncwor bolow:

A:

Q: Evaluate the following limits. x + sin(x) + 2vT x + sin(x) V1+x – 1 – 5 a) lim 2 b) lim r2

A: Given: a  limx→∞x+sinx+2xx+sinxb limx→01+x-1-x2x2

Q: 2. Use a table of function values to estimate lim in3x sin 3x sin3x -0.1 0.1 -0.01 b. 0.01 -0.001 c.…

A:

Q: In (x +h) – In (x) is When x = 2e, lim h→0 h

A: Substitute x=  2e above

Q: I. Evaluate the following limits. x sinh x 1. lim x-40 cos 3x – 1

A:

Q: Suppose if f(r) s g(x) < h(x) for all z€ (0, 2), what is lim h(x)? Select the correct response OA-1…

A: Solution: The objective is to determine the correct option for the given questions

Q: 2 dx In evaluating is same as evaluating lim cos ). Determine the value of f(x) if x=0.91 4 C- 2+

A: It is given that, ∫242xx2-4dxandlimc→2+cos-1f(x)c4 It is known that, ∫1xx2-1dx=sec-1x

Q: O Find lim (X,Y)→ LD,0) **+3y* or show it DNE.

A:

Q: 4. Use the sandwich theorem to find the following limits: sin x (a) lim cos x (b) lim

A: a) -1≤sin x≤1⇒-1x≤sin xx≤1x⇒limx→∞-1x≤limx→∞sin xx≤limx→∞1x⇒0≤limx→∞sin xx≤0⇒limx→∞sin xx=0(using…

Q: sin x – x (a) lim (b) lim (1+ x)/* 1/x

A:

Q: Find the limit. O 75 π O O' O O I 00 D8 - 150 lim sin¹. 5 x X→ 0 ¹7x

A:

Q: Computing the derivative of ƒ(x) = x2 ex

A: Consider the given function fx=x2ex

Q: (c) Prove the value of lim Sin 3a o Cos 4Do NOT use L'Hospital's Rule.

A: The given limit is,

Q: Use the graphs of f and g and their tangent lines at (2, 0) to find lim f(x) x+2 g(x) y4 y = 1.6(x -…

A: We need to evaluate the value of limx→2f(x)g(x) using the following graph

Q: It can be shown that lim be¯b = 0. Use this fact to compute S*xe* dx.

A: Given: ∫1∞xe-xdx

Q: Evaluate: limt o sin 3t t5 (t-1)² using L'Hôpital's

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Use the L' Hospital Rule to find : lim In ( csc? x) x → 3n (2 (x -37/2)2 lim Ja'y +a-a 8h - (1…

A:

Q: Find the limit. lim t-0 sin(6t) ; + e-tj + 4k i t

A:

Q: If ƒ' is continuous on [0, ∞) and lim→∞ f(x) = 0, show that I p'(x) dx = = -f(0)

A: First we will integrate then put limit

Q: If [ f(x)\dx<∞ show that limf(x)dx=0 k→∞00 1

A: We have to prove that given expression.

Q: tan z lim is Select one: a. e b. 0 с. 1 d. -1

A: Given limx→01xtan(x)

Q: Given n ≥ 0;  explain that   limx→∞ fn(x)/(e^x) = 0.

A:

Q: Evaluate using the Squeeze Theorem.

A: Given: limx→0 x sin 1x2  To evaluate: The limit using Squeeze theorem.

Q: Evaluate the following limits. x + sin(x) +2Vã x + sin(x) a) lim

A: NOTE***As per bartleby guidelines for more than one question, only first to be answered send other…

Q: 1 lim x sin x x2 x→0 O 1/5 O 1/7 О 16

A: Given, limx→01x sinx-1x2

Q: 70. J, f(x) dx may not equal lim , f(x) dx Show that 2x dx o x² + 1 diverges and hence that 2x dx x²…

A:

Q: Find the following limit limx→0 (1/sin x − 1/x)

A: limx→01sinx-1x=limx→0x-sinxx·sinx=0-sin00×sin0=00

Q: Find the limit of the following: lim     ln(tan(x)) x→π+

A: Given function is

Q: Find the limit. lim t 0 sin(t)

A:

Q: Consider the function f (x) = x(Va – 1), where a > 0, x > 0. If 0 < a < 1, show that limx0f (x) is a…

A:

Q: If f(a) = 0 and f'(a) = 6, find lim la + h) 2h %3D %3D

A:

Q: The graph of a function f and its tangent line at 0 are shown. What is the value of lim X→0 e7x f(x)…

A:

Q: Evaluate the limid lim X'sin t X→o sin x?

A: We have to find limit

Q: Calculate the following limits. cos x 1) lim (tan x)cos* x² – sin?2x 2) lim x→0 x2

A:

Q: Please show step-by-step solution

A:

Q: 1. Show that for all f e L'(R) lim da = 0.

A:

Q: Find the limits

A:

Q: S, f(x) dr may not equal lim , f(x) dx. Show that 2x dx x* + 1 diverges and hence that 2x dx ? + 1…

A:

Q: If f' is continuous on [0, ∞) and limx→∞ f (x) = 0 , showthat

A: Given, If f' is continuous on the interval [0,∞) and limx→∞f(x)=0 show that, ∫0∞f'(x)dx=-f(0)

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.