8. Show lim tanh x =1 X→∞

Q: Inx lim =? x→1 x-1

A: Given: limx→1lnxx-1

Q: 5. lim tan x cos y = 1 (x,y)→(,0)

A: To show :  lim(x,y)→π4,0tan x cos y = 1

Q: Suppose that in the interval 7 ≤ x ≤ 19 you know that f'(x) is positive and f(x) is negative. Select…

A: Suppose that in the interval  7≤x≤19  you know that f'(x) is positive and f''(x) is negative.

Q: VI – 1 а. lim r→1 Vx + 3 – 2 1 – sin x b. lim COS x 2 2

A: To evaluate the given limits without using L'Hospital rule.a limx→1 x3-1x+3-2b limx→π2 1-sin…

Q: If f is continuous from the right of x1 and lim f (x) exists, then lim f'(x) = f'_ (x1). O True…

A: it is true

Q: ,3x lim x→0 CO cosh(Зa)

A: By substituting cosh(3x) in givenimit we can get the required value of Function.

Q: lim x30 VI+x 1+% ㅈ _/

A: L=limx→01+x−1x

Q: 10" – 5* - lim sinx O In(2.00) O In(50.00) O In(5.00)

A:

Q: 16. If f is differentiable at xo, prove that lim h→0 f(xo + αh) - f(xo - ßh) h = (x + ß)ƒ'(xo).

A:

Q: If f' is continuous, f'(2) = 7, and f(2) = 0, then

A:

Q: X'+2X Lim メーロ 0 @ True eflase laşe 8.

A:

Q: Using the limits sin h lim h→0 h - 1 and cos h lim h→0 h - 1 as facts (which do not need to be…

A:

Q: Use L'Hopital's rule to evaluate lim(1 – 2 sinh(x)) sch(a).

A:

Q: Let f(x) = x²sin () for x + 0 and f (0) = 0. b) Use definition 6.1.1 to show that fis differentiable…

A: Solving by definition of 6.1.1 we have

Q: 9. lim 15 1 + (i/n)6

A:

Q: f(xn) f(xn-1) xna, prove that lim |C| = 1. n→∞ 5. Consider Cn = ƒ'(ïn-1). Under the assumption that…

A: The given sequence Cnn=1∞ is defined as ; Cn = fxn f'xn-1fxn-1 f'xn  and  f'(α) ≠ 0  and xn → α…

Q: Use the graph of f(x) below to evaluate the given integrals: a. xp (x)f*J q c. f) dx d. f) dx Lf) dx…

A:

Q: If 1/(x^2 + 1) ≤ f(x) ≤ 1 + x^2 for all x in the interval (−1, 1), what is lim x→0 f(x)?

A: Please refer the attached image for complete solution.

Q: Evaluate the following limits (sin(5h) а. lim h→0 4х ´sin(5h)` b. lim h→o \sin(4h). ´tan(5h)` С. h→0…

A:

Q: 4. L0-dx= (A) lim (3- 4)Ax, (B) lim 3-x)2 (C) lim (3-) 8. (D) lim (3- u)

A:

Q: Why is limx→0(cos(x2))=0 but limx→0(cos(x-2)) is not defined?

A: We have to show  but  doesnot existNote: It is given  which is incorrect,  is correct

Q: Find lim arctan x→∞ X - – x³ x + 7

A: limx→∞arctanx-x3x+7

Q: 10 - (*;")" 1/t 2' +3' f(t) = for t + 0. 3 lim f(t) =

A: The given function is ft=2t+3t31t  for t≠0. Find the limit value limt→+∞ft. Limit of the…

Q: Theoretical assignment Consider hyperbolic tangent function

A: Given,                f(x)= tanh(x)=ex-e-xex+e-x,     x∈-2, 2and cut the interval -2, 2 into 4…

Q: lim lnxln(x-1)=? Use L'Hospital's Rule

A:

Q: lim f(x) where f(x) = x→1+ X, x ≤1 1-x, x>1'

A: