Proving identities Prove the following identities. sinh (x + y) = sinh x cosh y + cosh x sinh y

Q: Derivatives involving trigonometric functions Calculate dy>dx forthe following functions.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: sine de Q.4 Evaluate the following integral : cos sin

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the next…

Q: sin² sin'x =-COSr 2. 0, 2.

A: To solve for x , where x should lie in the interval  [0,π/2]

Q: onsider the functions f(x) = 2 sin(3x), g(x) = cos(x²), and h(x) = tan(r*).

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Q: Fourier Senies fra) = x² x e[-1,7]

A: We have to solve given problem:

Q: Hyperbolic Functions Investigate the shape of a wire (eg. power line) between two points at the same…

A: It is given that,  sinh(x)=ex-e-x2 and cosh(x)=ex+e-xh

Q: Find the limits

A: Our Aim is to find the limits of the following expression given below:-limx→0 sin (x) cot (2x) -(i)

Q: (tanz+cotr)-(tan'r+cos'r)-(sin'z+cot'r) -dz S x Lnx Ln (Lnx) Ln (Ln (Ln(x))) Ln (Ln (Ln (Ln(x)))) Ln…

A: On solving numerator we get equals to 1 and then solve by substitution

Q: Proving identities Prove the following identities.

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Q: Using Symmetry Use the symmetry of the graphs of the sine and cosine functions as an aid in…

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

Q: Find the limit.

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Q: Define the following hyperbolic function directly in terms of the exponential function (i) tanh(x)

A: Defining tanhx

Q: sinhr²-² 2 1. lim r+0 sinhr−r

A: To evaluate: limx→0 sinh⁡x2−x2sinh⁡x−x Given limit is of 00 form L'Hospital's rule tells us that if…

Q: sece-cos e The simplified form of is sece+cose

A: We will simplify as following.

Q: SUM/DIFFERENCES IDENTITIES sin (a + B) = sin a cos ß t cos a sin B %3D cos(a + B) = cosa cos B F sin…

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Q: S tan36x sec106x dx

A: I=∫tan36xsec106xdx=∫tan26xtan6xsec106xdx=∫sec26x-1tan6xsec106xdxLet sec6x=u…

Q: / [sec-(x) – csc²(x)]dr Evaluate: A e (x) - c«°(x) + C sec an(x) – cot(x) +C B esc (x) + sec³(x) + C…

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Q: Evaluate cos x dx sin? x t²-2t4 -dt t4

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Q: Deriving hyperbolic identitiesa. Use the fundamental identity cosh2 x - sinh2 x = 1 to prove that 1…

A: It is known that cosh2 x - sinh2 x = 1. Now divide cosh2 x on both sides of the above equation and…

Q: e -e * Let tanh x and arctanh x be its inverse. Compute (arctanh x)'. e +e I

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Q: 8. [sin? x cos' x dx Ssin*

A: (8). Given: I=∫sin2xcos5xdx   As we know from the trigonometric identity; sin2x+cos2x=1 And The…

Q: 101–104. Verifying identities Verify the following identities. 101. sinh(cosh| x) = Vr? – 1, for x =…

A: 101). To verify the identity: sinhcosh-1x=x2-1,for x≥1. Verification: Let θ=cosh-1x⇒coshθ=x. We have…

Q: Critical points Find the critical points of the function f(x) = sinh? x cosh x.

A: The given hyperbolic function is: f(x)=sinh2x coshx To find the critical point of this function,…

Q: Verifying Expressions Are Not Equal Verifythatsin(t1 + t2) ≠ sin t1 + sin t2

A: The objective is to prove Sint1+t2≠Sint1+Sint2 Consider the value of t1=30∘ and t2=30∘ Find the…

Q: sin x) dr Evaluate: sin(x) + 1 1- sin(x) A +x+C cosx 1+ sin(x) B cos(x) x+C (c) cos(x) +C cos(x) - x…

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Q: 20. A certain substitution gi

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Q: Beta Function sin n l9, (h) cos 9 sin ele. Ans. (a) 16/15. (b) 8/105 Evaluate (a)

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Q: J I+ sin(x) sin(x) xp. Evaluate: 1– sin(x) A -2x+C cos(x) 2( sin (x) – 1] cos(x) B -x+C 4cos(x) + C…

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Q: Home work: find the root f(x)=3x – cos(x) -1=0

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Q: Trigonometry, and Inverse Trigonometry Sx* (a² + x²)% dx

A: ∫x3a2+x212 dx Put, x=atanθ⇒dxdθ=asec2θ⇒dx=asec2θ dθ

Q: raph function of the form y=a sin (wx)  i dont understand any of it

A: To graph function of the form y=a sin (wx)

Q: sin'x Evaluate the integral dx sin'x+cos°x

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Q: sin(x) dr Evaluate: sin(x) + 1 |- sin(x) cos(x) A +x+C 1+ sin(x) B -x+C cos(x) CoS cos(x) -+C cos(x)…

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Q: cos®0 d®

A: We will first derive Waill's formula. ∫0π/2sinnx dx=∫0π/2cosnx dx. Since, ∫0π/2sinnx…

Q: Variable Separable DE involving Trigonometric Functions ) (eay -y) cos cx) dy e sin ax

A: The given differential equation is,e2y-ycos(x)dydx=eysin2x

Q: () Sec A sec A + tan² A sec A - | 1 CSC X = COs X cot *x + sec?x +1 Il

A: " Since you have posted two questions, we will solve first question for you. To get another question…

Q: sin h Let f(x) = sin x. Show that: S(x+h)-f(x) - sin x • 1-cosh = co This formula will be used…

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Q: cosh a Example. Use u-substitution to find an exact value of dx. V1+ sinh x FOLUTION

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Q: 4. |3 cos(2.x – / 2) cos(x+ 7 /4)dx -

A: Use substitution method to integrate the function. Substitute u=x+π4 in ∫ 3cos2x-π2cosx+π4dx. ∫…

Q: sen x + cos' x = 1. 1. cos x= sen x = Ltransformar la expresión dada e

A: To find the value of sin (x) we will use given Identity.

Q: sin (sin h) 36. lim h→0 sin h

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Q: Composition containing sin x Suppose ƒ is differentiable on[-2, 2] with ƒ′(0) = 3 and ƒ′(1) = 5. Let…

A: Given f'0=3, f'1=5 and gx=fsinx. Chain rule of differentiation states that: ddxfgx=f'gxg'x…

Q: thẻ identity algebraically. Use the table feature of a graphing utility to check your 1 + sin(0)…

A: Solve the following

Q: Csc z - sin x cot z csc a

A: our objective is to prove the identity

Q: | cose · sin®e de COS

A: Integration is a tool in calculus used for finding area of curve. It can be indefinite where area of…

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

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Q: ce z = cos(xy)+æ²y

A: Solution

Q: Differentiate y= sin (3x +1)

A: Given: y=sin-13x5+13

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.