मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

If f'(x) = x–1, then find f(x) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

If f'(x) = x–1, then find f(x)

बेरीज

उत्तर

Given, f'(x) = `1/x`

On integrating both sides, we get

f(x) = logx + C

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2021-2022 (March) Set 1

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

`tan^(-1) sqrt3 - sec^(-1)(-2)` is equal to ______.


Find the value of the following:

`cos^(-1) (cos  (13pi)/6)`


Find the value of the following:

`tan^(-1) (tan  (7x)/6)`


Evaluate the following:

`tan^-1(tan  (5pi)/6)+cos^-1{cos((13pi)/6)}`


Find the set of values of `cosec^-1(sqrt3/2)`


Find the domain of `f(x)=cotx+cot^-1x`


Evaluate the following:

`cot^-1  1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`


Evaluate the following:

`tan^-1(-1/sqrt3)+cot^-1(1/sqrt3)+tan^-1(sin(-pi/2))`


Evaluate: tan `[ 2 tan^-1  (1)/(2) – cot^-1 3]`


In ΔABC, if a = 18, b = 24, c = 30 then find the values of cos `A/2`


Find the principal value of the following: cosec- 1(2)


Find the principal value of the following: tan- 1( - √3)


Find the principal value of the following: cos- 1`(-1/2)`


Evaluate the following:

`"cosec"^-1(-sqrt(2)) + cot^-1(sqrt(3))`


Prove the following:

`sin^-1(3/5) + cos^-1(12/13) = sin^-1(56/65)`


Prove the following:

`cos^-1(3/5) + cos^-1(4/5) = pi/(2)`


Prove the following:

`tan^-1(1/2) + tan^-1(1/3) = pi/(4)`


Find the principal solutions of the following equation:

sin 2θ = `− 1/(sqrt2)`


Find the principal solutions of the following equation:

cot 2θ = 0.


sin−1x − cos−1x = `pi/6`, then x = ______


The principal value of cos−1`(-1/2)` is ______


If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______


Evaluate:

`sin[cos^-1 (3/5)]`


Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`


Evaluate `cos[pi/6 + cos^-1 (- sqrt(3)/2)]`


If tan−1x + tan−1y + tan−1z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1


Prove that cot−1(7) + 2 cot−1(3) = `pi/4`


Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`


Find the principal value of the following:

`sec^-1 (-sqrt2)`


Solve: tan-1 (x + 1) + tan-1 (x – 1) = `tan^-1 (4/7)`


Express `tan^-1 ((cos x - sin x)/(cos x + sin x))`, 0 < x < π in the simplest form.


Find the principal value of `cos^-1  sqrt(3)/2`


Find the principal value of cosec–1(– 1)


Find the principal value of `tan^-1 (sqrt(3))`


In ΔABC, tan`A/2 = 5/6` and tan`C/2 = 2/5`, then ______


In Δ ABC, with the usual notations, if sin B sin C = `"bc"/"a"^2`, then the triangle is ______.


sin[3 sin-1 (0.4)] = ______.


The value of 2 `cot^-1  1/2 - cot^-1  4/3` is ______ 


If sin `(sin^-1  1/3 + cos^-1 x) = 1`, then the value of x is ______.


The value of cot (- 1110°) is equal to ______.


If `3sin^-1((2x)/(1 + x^2)) - 4cos^-1((1 - x^2)/(1 + x^2)) + 2tan^-1((2x)/(1 - x^2)) = pi/3`, then x is equal to ______ 


The value of `sin^-1(cos  (53pi)/5)` is ______ 


`sin{tan^-1((1 - x^2)/(2x)) + cos^-1((1 - x^2)/(1 + x^2))}` is equal to ______ 


`cos^-1  4/5 + tan^-1  3/5` = ______.


Solve for x `tan^-1((1 - x)/(1 + x)) = 1/2 tan^-1x, x > 0`


The domain of the function y = sin–1 (– x2) is ______.


Show that `2tan^-1 (-3) = (-pi)/2 + tan^-1 ((-4)/3)`


Prove that `tan^-1  1/4 + tan^-1  2/9 = sin^-1  1/sqrt(5)`


All trigonometric functions have inverse over their respective domains.


`"cos"  2 theta` is not equal to ____________.


If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA "n" in "I"`, then x = ____________.


If tan-1 3 + tan-1 x = tan-1 8, then x = ____________.


If tan-1 (x – 1) + tan-1 x + tan-1 (x + 1) = tan-1 3x, then the values of x are ____________.


The range of sin-1 x + cos-1 x + tan-1 x is ____________.


`sin[π/3 - sin^-1 (-1/2)]` is equal to:


If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA  "n" in "I"`, then x = ____________.


`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.


If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt "cos" alpha) = "x",` then sinx is equal to ____________.


If a = `(2sin theta)/(1 + costheta + sintheta)`, then `(1 + sintheta - costheta)/(1 + sintheta)` is 


If |Z1| = |Z2| and arg (Z1) + arg (Z2) = 0, then


Domain and Rariges of cos–1 is:-


What will be the principal value of `sin^-1(-1/2)`?


What is the principal value of cosec–1(2).


Find the value, if sin–1x = y, then `->`:-


`tan^-1  (1 - x)/(1 + x) = 1/2tan^-1x, (x > 0)`, x then will be equal to.


Value of `sin(pi/3 - sin^1 (- 1/2))` is equal to


What is the values of `cos^-1 (cos  (7pi)/6)`


Assertion (A): The domain of the function sec–12x is `(-∞, - 1/2] ∪ pi/2, ∞)`

Reason (R): sec–1(–2) = `- pi/4`


If θ = `sin^-1((2x)/(1 + x^2)) + cos^-1((1 - x^2)/(1 + x^2))`, for `x ≥ 3/2` then the absolute value of `((cosθ + tanθ + 4)/secθ)` is ______.


Consider f(x) = sin–1[2x] + cos–1([x] – 1) (where [.] denotes greatest integer function.) If domain of f(x) is [a, b) and the range of f(x) is {c, d} then `a + b + (2d)/c` is equal to ______. (where c < d) 


cos–1(cos10) is equal to ______.


`cot^-1(sqrt(cos α)) - tan^-1 (sqrt(cos α))` = x, then sin x = ______.


If sin–1a + sin–1b + sin–1c = π, then find the value of `asqrt(1 - a^2) + bsqrt(1 - b^2) + csqrt(1 - c^2)`.


If ax + b (sec (tan–1 x)) = c and ay + b (sec.(tan–1 y)) = c, then `(x + y)/(1 - xy)` = ______.


If x ∈ R – {0}, then `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2)))`


If tan–1 2x + tan–1 3x = `π/4`, then x = ______.


The value of `cos^-1(cos(π/2)) + cos^-1(sin((2π)/2))` is ______.


If 2 tan–1 (cosx) = tan–1 (2 cosec x), then sin x + cos x is equal to ______.


Prove that:

tan–1x + tan–1y = `π + tan^-1((x + y)/(1 - xy))`, provided x > 0, y > 0, xy > 1


Solve for x:

5tan–1x + 3cot–1x = 2π


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×