lim (x)-(.0) tan , -= (A) Does not exist (B) e? (C) 0 (D) ezn (E) e *IN

Q: lim (1-cos x1/2) / ln(1+x) ? x-->0+

A: Here we use the series expansion of the functions cos (x) and ln(1+x):

Q: f(x) = { cos x, xpi  which lim does not exist

A:

Q: Let COS X if x 0 %3D | (a) sketch the graph of f (x) (b) Is f (x) continous at x = 0? Give reason/s…

A: f(x)=cos x         if x<00                 if x=01-x2         if x>0

Q: Let Find f(x)\x= = ". y = f(x) = 31 sec x + 18 tan x 31 sec x 18 tan x d dx -f(x)\ x= 1 *

A:

Q: csc(x) – 1 sec(x) Differentiate: f (x) = (A f'(x) = - csc²(x)+ sin(x) B B f'(x) = - csc2(x) – cos(x)…

A: We can use differentiation of trigonometric function rules to find the derivative of the given…

Q: For n 4 we find the derivative of f(x) = x* as follows: f(x + h) - f(x) (x + h)* – x lim f'(x) = lim…

A:

Q: 1/a | sin(t")dt Find lim T.

A: We have to calculate the value of : limx→∞∫01xsint2dt·x

Q: Find Integral (cos(x) cos (2x) cos (5x) dx : considering cos (mx) cos (nx)= = (cos((m-n)x)+ cos…

A:

Q: lim x→0 (sin10(x)cos(8x))/x=?

A:

Q: x2-8x+15 ; x 3 a) If f(x)= 2x-6 is continuous at x=3, then find the 2-5 ;x=3 value(s) of k. sinx b)…

A:

Q: S cos (z +1) z<-1 -1<z Let F (x) : e -1 Then lim F (1) =

A:

Q: an=(tan-1(n))/n, limn->infinity an=?

A: limn→∞ arctannnlimx→afxgx=limx→afxlimx→agx,   limx→agx≠0=limn→∞ arctannlimn→∞ n=π2∞ Apply…

Q: Suppose f(x) = 3*sec(3*) tan( 3*). Evaluate: / s(x)dx sec(3*) A +C In (3) 3*. sec(3*) +C B In (3) ©…

A:

Q: Let G(z)- sec 0 de for z in [0, 1]. Find G" (z).

A:

Q: 3-f(x) = tanh¯1(cos(e*))

A:

Q: e2x tan xy = lim (x.y)-) %3D (A) Does not exist (B) e2 (C) 0 (D) e2 (E) e

A:

Q: 9. lim ln (1-cos x) x->0

A: To find:-

Q: lim cos(x) x- (7/2)* 1 - sin(x)

A:

Q: Let h(x)= f(g(x)) where f(x)=tanx. Then h'(x)= a) f'(tan x) g'(x) b) g'(x)tan(g(x)) c) g(x)…

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Q: ex+e¬x_x²-2 3. lim X--0 SIN²X-x2

A: The given limit  limx→0ex+e-x-x2-2sin2x-x2 This limit is in 0/0 form, so we can apply L' Hospital's…

Q: 17. Applying the quotient rule, what is the correct FIRST STEP in finding the derivative of the…

A:

Q: lim t →0  (e^6t i + (sin(7t)/ (7t)) j + e^−4t k)

A: Limit :

Q: 2 lim(cosx)x² =? x→0

A: Given: limx→0cosx2x2=limx→0cos2x2x

Q: cos(2x)– cosx sin x 4. lim, »o

A:

Q: What are the intervals of monotonicity of f(x) = arctan (2(x-1)) - ln IxI ?

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Q: Evaluate / tan*(x) sec*(x) dæ.

A: I=∫tan3(x)sec2(x)dxsubstitute  tanx=udiffrentiatesex2xdx=du

Q: • Find f(22) (0), for f(0) = 2 cos(30), using pattern recognition. (Don't take 22 derivatives!) What…

A: The given function is fθ=2cos3θ.

Q: 5) Write 5 sinh x + 7 cosh x in terms of e* and e-* (A) 12e* - 12e-* (B) 12e* + 2e-* (C) 6e* + e-*…

A: To write the given trigonometric expression in exponential terms.

Q: sin(xy} lim (x.y) (0.0) t² + y

A:

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.