sin h Let f(x) = sin x. Show that: S(x+h)-f(x) - sin x • 1-cosh = co This formula will be used frequently in a calculus class.

Q: Integrals Evaluate each integral.

A: Given data:     The given integral is: . Assume 1+coshx=u and differentiate it with respect to x.

Q: sin x Let g(x) = . 1 Find the derivative a'(x). dt . 2 1+t3 cos? x 1+ sin x sin x 1+ cos³x cos X 1+…

A:

Q: sin(2n - 1)x sin nx If dx, then prove that sin x 2 sin x U -U, =: -1, =U and find 1, = 2

A: The expressions are Un=∫0π2sin2n-1xsinxdxtn=∫0π2sin2nxsin2xdx We have to prove,…

Q: sin²(x) + sin(x) dx To evaluate the using basic formula of integration (without using cos²(x)…

A:

Q: sin 5x 6. lim x→0 sin 10x

A:

Q: COS x Find values of x in [0, 27] for which f(x) = has a horizontal tangent. 2+ sin x

A:

Q: (sin x - cos x )² + 2cos x sin x

A: To simplify trigonometric expression

Q: sin x cos x-1 %3D COs x+1 sin x

A: sin xcos x +1+cos x -1sinx=0

Q: evaluate the limit.

A:

Q: * sin²(x) + sin(x) cos²(x) To evaluate the -dx using basic formula of integration (without using…

A:

Q: sin x(cos x-1) 8. Prove sin(n -x) – tan(t + x) | COSX

A:

Q: A sine reduction formula Use integration by parts to obtain a reduction formula for positive…

A: Given to obtain a reduction formula for positive integers n, by using integration by parts for…

Q: sin(x) 4. lim x→0 1 – cos(2x)

A: The solution of the problem is given in the next step.

Q: Verify the identity:

A:

Q: lim ea+sin() where a > 0 is a constant.

A: Given, limx->inf ea+sin(1/x) where, a>0 is a constant.

Q: (sin æ)(1 – cos æ) lim COs x x→0 x2

A:

Q: sin(x) Evaluate dx. cos (x) – cos(x) – 2 |

A:

Q: sin 2x dx Evaluate the definite integral: COS X

A:

Q: (cos x-1)(1+cos(-x))=-sin' x

A: cosx-11+cos-x=-sin2x

Q: sin x-1 lim cos x 2

A: Answer and explanation is given below...

Q: sin 3x 1. Find lim x→0 sin 4x

A: Hello, thank you for the questions. We’ll answer the first question since the exact one wasn’t…

Q: Sin 10. Im sin ax 12.lim X-0 sinbr X-0

A: We have to find

Q: sin(2 – x) (d) lim +2 x2 - x - 2 2x sin r (e) lim 140 1 – cos 4.x sin x – sin 1 (f) lim x - 1

A:

Q: sin () if x + 0, COS X Let f : R → R be the function given by f(x) if x = 0. -1

A: The function  f:ℝ→ℝ is defined as follows: fx=sin1xcosx  if  x≠0-1                    if  x=0…

Q: ´sin x-sin x cos x lim x2

A: This can be evaluated as follows:

Q: Find the limit

A:

Q: sin(3x) 6)lim x→0 sin(4x)

A: We have to evaluate the value of limx → 0 {sin(3x)/sin(4x)}

Q: sin x 16. Evaluate f dx cos²x a. tan x sec x + C b. sec x c. sec?x d. tan x

A: Using substitution method Let cosx =t

Q: . sin 2x cos x+ cos 2 sin x = 12

A:

Q: sin x.cos x 1+ 2.In x

A:

Q: sin2(x) + sin(x) cos2(x) To evaluate the -dx using basic formula of integration (without using…

A:

Q: Find the limit

A:

Q: Prove the identity. cosh(-x) = cosh(x) (This shows that cosh is an even function.) cosh(-x) = | |…

A: we have to find

Q: sin(3x) 6)lim x0 sin(4x) 4.a

A: By using the L. Hospital's law we will solve the given limit

Q: lim (sin 2x-sinx)= sin x 26. %D A 0. B -3. C 2. Đ 1.

A: To find the given limit, limx→0sin2x-sinxsinx Using the trigonometric identity, sin2x=2sinx.cosx…

Q: sin x lim 1-e* x→0

A: Given query is to find the limit of the expression.

Q: sin e, sine cose cose 1 tan 2 0 O2 cot 0 2 tan 0

A:

Q: cos x F(x) = sin-1 1+sin x. F(x) = In ln In x

A:

Q: sin 7x 9. lim 9.h x→0 sin 3x

A: GIVEN limx→0sin7xsin 3x

Q: (sin x +cos x)^2 =1+sin x cos x

A:

Q: sin(2x²)+x³ . Let f(x) = 0, df if x + 0 Then find- if x = 0 dx x=0

A:

Q: sin(6x) Evaluate: lim 1-oL sin( 4x) A B0 1

A: we have given that limx→0[sin(6x)/sin(4x)]

Q: sin-1 x = cos s-'(1 – 2x²) x > 0. |

A: The above problem is solved.

Q: sin x b. 1+cos x 1-cos x sin x

A:

Q: / [cos(x) – sin(x) ]dx Evaluate: A -cos(x) + sin(x)+C B ® cos(x) – sin(x) +C © - cos(x) – sin(x)+C D…

A: We know that integration of sinx is -cosx  And integration of cosx is sinx. Here i attached solution…

Q: " sin²(x) + sin(x) cos²(x) To evaluate the -dx using basic formula of integration (without using…

A:

Q: sin x 25) lim x→0 5x 3(1 – cos x) 26) lim sin x (1 – cos x) 27) lim 2x2

A:

Q: sin x -dx = 5. 2- cos x A. – In(2) В. — Iin(3) c. In(3) D. 1-In(3) Е. In (3)-1 С.

A: Given: The integral  ∫0πsinx2-cosxdx