2) [ tan' (-) sec" () dx , 3) | 3) T5x+4 dx, 1) sin-1x dx , tan () sec? V5x +4

Q: 4) Estimate tan (0.5) using the tangent line to y = tan(x) %3D 6

A:

Q: Integrate sin^2(7x)-cos(x)

A:

Q: Find the derivative of O2 sec 2x O 2tan 2x O-2 cot2x O 1/cos2x y=In sin 2x

A:

Q: What is the resulting integrable form after you applied substitution technique in tanx sec“x dx?

A:

Q: Integrate: S tan (æ) sec³(x)dx

A:

Q: Find dy/dx  if  4 cosx siny = 1

A: We will directly differentiate it.

Q: 29. [sin (9y)sec (9y)dy

A: Use the formula sin2x + cos2x =1.

Q: What is the integral of question 23 and why is the answer 0?

A: Let f(t)= t^4*tan t/(2+cos t)

Q: 2 iii. sech x3 tanh( x3 S- -dx 1 X3

A:

Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 + 8 8 sin(3x)cos(3x) , sin(2x)cos(2x)…

A: We need to evaluate integral.

Q: aie of sin(4x)+8 cos(x)+2x2 cos(4x)+8x sin(4x)+.

A:

Q: Find an equation of the tangent line to y sin 2x = x cos 2y at the point π/2 , π/4 . Do not…

A: First we will find Differentiation of given equation to get slope of the tangent line. Now equation…

Q: 13. Find the derivative at x = a for f(x)= /sin(4x) 2 Vsin(4a) cos (4a) Jsin(4a) 2 sin(4a) Vsin(4a)…

A:

Q: 13. To evaluate S - 3cos²x=1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+ csc²x)dx…

A:

Q: 11. Integrate. a. x3 b. S(5 tan 3x – 2 sec2 x)dx

A:

Q: f6)= Sin () (x 3x26x-8) 1 CosX In Ceos x) | $66)=Sinx+t Cosx. sinsetl -6()=DSin -2053 2.

A:

Q: 9.) JE sin°(x)cos*(x)dx 11.) F sin°(x)cos²(x)dx 2

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: d Verify tanh - = X 1- x2 dx

A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…

Q: Compute integral sin(cos(x^2)) sin(x^2)x dx

A: Explanation is given below...

Q: Evaluate: S Arctan 2 sin²x dx . Arctan 1 cos+x

A: Given,  ∫Arctan1Arctan2sin2xcos4xdx

Q: 1+ tanx y = logy 1- tanx prove that 9 = sec2x dy dx

A: Given,           y=log1+tanx1-tanx

Q: 1) Find the derivative of f(x) = 1+sin 2x %3D 2 cos3 x

A:

Q: find dy/dx 4x -x 2x 23) y= Sin- +x².Sec 2-x + 2x.Sec) 2 (ans.: (2-2»N(2-x² - x* 4 4

A: To find the dy/dx means y' of the given function

Q: The first derivative of y = sin( 4x + 3) is %3D а. - 4 cos(4x +3) b. 4 cos(4x +3) С. cos(4x+3) d. -…

A:

Q: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: roo sin(2) Compute (4) dx. fo x(x²+4)

A:

Q: From 0-2 sin(x^2) dx using trapezoidal rule with n=4 as well as midpoint rule with n=4

A: Trapezoidal rule=∫02sin2(x)......(1)As we know that accoding to trapezoidal rule…

Q: 3- - 플 플 sin²cyl y จน

A:

Q: 2cosx dx 5- f 1+(sinx)2 a)2 tan sinx| b) 2 In sinx| c)2 In(1+ (sinx)1

A: We use Trigonometry substitution method

Q: i) S'(2x – 1)* dx (In x)2 j) fth dx 7 k) S (1-- -)dx (x2+1) 1) S(1+ tan² x) dx

A: I am attaching image so that you understand each and every step.

Q: Find* esin ¤ dx tan x csc x cos x e $in xt. - cos x e Sin x + c Option 4 Option 2 esinx + c ,sin.…

A:

Q: Use differentials to estimate sin (π/6 + 0.01).

A: Use differentials to approximate the value of sinπ6+0.01 The nearest number to sinπ6+0.01 whose sine…

Q: 15. -- sin(2+ 2) dz

A: According to the given information, it is required to solve the give integral.

Q: 13. To evaluate f 2costx-1 dx, the integrand can be transformed to 1-sin²x a. [(3cos³x+csc²x)dx b.…

A: Here we have to transformed the given integrand.

Q: Exercises to solve: 1. fx² In(x + 1) dx 2. (x2 + x – 2).cos4x. dx 3. Se-*sinxdx 4. S sinh2x.cosh5x…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The second derivative y" of y = x3 + ex – sin(2x) is . 1. O y" = 6x + eX – 8 sin(2x) 2. O y" = 3x +…

A:

Q: solve  sin(x)dy/dx + ycos(x) = cos(x)[ex + sec2(x)].

A: Convert into dy/dx+p(x) y=Q(x)

Q: 1-f²₁ ¹/²(y² sinx dx dy) 2-√²-dxx2 0 3- f(cscx cotx)² 2 4- f₁² x (x − 3)dx for 5-S²₂ (x³ + √x) dx

A: 1.

Q: Evaluate sin (4x) cos -2(4x) dx. | sin (4x) cos -2(4x) dx = O

A:

Q: Find the derivative dy/dx of y = cos 3x O 3 sinx О З cosx O 3 sin 3x О З сos 3x none of the above

A: We can do this by doing derivative both side.

Q: 4. S tan x dx CSC X sec (In x) dx 5. dx 6. S; 1- cos 2x

A:

Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A: Show that, z''+4z'+8z=0 if z=e-2xsin2x+cos2x Formulas used:…

Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: Find the equation of the line tangent to f(x) = cos² x – sin²| %3D at x = 6

A:

Q: when

A:

Q: 29. (csc x – sec x)(sin x + cos x) dx find + In 5 ) dx 30. 3 sinh .3 2x3 V1 + x² sin x dx 32. 31. dx…

A:

Q: 3. SIX f- - dx x in x√√(inx)2-9

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Q: dz 5 – 2x cos 2x dx 1 + sin 2x sec² 0 de. tan 0

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.