P. Iff: [-4,0]→R is defined by e* + sin x, its even extension to [- 4, 4] is given by (a) – e-lx| - sin|x| (c) e-lxl + sin| x| (b) e-lx| – sin|x| (d) - e-lx| + sin|x|

Q: 1 (a) lim 2x+sin x 5x+2 (b) lim 1 (c) lim cos -

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Graph f(x) = sin x, g(x) = cos 2x, h(x) = ( f - g)(x) in the same rectangular coordinate system for…

A:

Q: Evaluate f{ [sec (x) + csc (x)] + sin ()} dx : (2)]? + sin (팔프)}dz O a. tan (x) In |csc (2æ) + cot…

A: To solve the following integral

Q: 10. Given: f(x) 3= d) tan(A – B) and g(x)=x² +8 x- 5 Find: a) (f-g)(x) (g •(8))(x) i) (g-f)(3) b)…

A: Given that f(x)=1x-5 and g(x)=x2+8   (a) f-gx f-gx=fx-gx               =1x-5-x2+8…

Q: Show that f(r) = O(|x – xo|*) and g(x) = o(]x – roP) imply f. g(x) = o(|x – xo]k+i). - -

A:

Q: x²+1 lim tan (x,y) → (0,1) x? +(y-1)². O is equal to 0. O is equal to -II

A: Given that: lim(x, y)→(0, 1)tan-1x2+1x2+(y-1)2

Q: lim cos x+4e* is 5er

A:

Q: Apply the special case of the general power rule d/dx [h(x)]2 = 2h(x)h(x) and the identity fg =…

A: dhx2dx=2hx·h'x  &  fg=14f+g2-f-g2

Q: Let f(x)=2x-3,g(x)-5x, and h(x)=x2 what is the sinpliest fornm of h(x)*g(f(x))

A: Explanation of the solution is given below...

Q: What is the range of f(x) = cos¯¹(0)? A [-] 2 2 B [0, π] C [-1,1] D (-∞, ∞)

A:

Q: If f(2010) = π/2, f(2x) = f(x)Vx E R and f(x) is continuous for x E R, then the value of…

A: Let us solve above problem by using L'Hopital rule

Q: Let f"(x) = x'/A cos(x), /(0) = 2, and f(1) = 2. Is it true or false that 7=-73+ cos(x) + 28…

A: The answer of above solution is option A. i.e true.

Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

A:

Q: 2 cos(5x) – 5 x² – 2 lim sin(3x) – x² – 3x - - (Write your answer in the given box)

A: We will use L'Hopital rule

Q: If g(x) = Cos x – Sin x a) Find g() and g (#) 8 b) Show that g ( - + x) = g(n – x) .2

A: sin(π2+x)=cosx cos(π2+x)=-sinx sin(π-x)=sinx cos(π-x)=-cosx

Q: (е2х-1)2 dx е 2х

A: topic - indefinite integral

Q: (b) Suppose that f(x) = 2x^2 − x^4 . Find the intervals on which f is increasing and those on which…

A: Question no. (b):Suppose that To find the intervals on which is increasing and those on which it is…

Q: x + sin 2x lim x-2 x – sin 2x О з O 2 O 1/3 О 12 O other:

A:

Q: Find lim n→∞ n + cos(x) Jo ne + sin(x) So -dr.

A:

Q: (a) Let f(x) = cos(3x – 2). Find f"(x). (39) %3D (b) Let g(x) = 2***. Find g (153) (x). %3D

A: Topic = Derivative

Q: Evaluate 2х— 7 -dx J x2 — бх + 10

A:

Q: A function f is even if f(x) = f(-x) and odd if f(x) = -f(-x). For example, f is even if f(x) = x2…

A:

Q: (x²–1)dx S (x++3x² +1)[tan-1 x2-1 aluation of is

A: Given integral is I=∫x2-1x4+3x2+1tan-1x2+1xdx To evaluate I Now, dividing the numerator and…

Q: (1) Use the definition to prove that if xn → 2 then (2xn + 1) / xn → 5/2.

A: As per our company guideline we are supposed to answer only first three  qs, kindly post remaining…

Q: (x²–1)dx (x2 – (x*+3x² +1)[tan-1 The evaluation of is In |tan-1| + e -In |tan-| + c (i) (ii) (iii)…

A: To find the correct answer, we will differentiate the option one by one and check which matches the…