If m is the slope of a tangent to the cu...

If `m` is the slope of a tangent to the curve `e^y=1+x^2,` then `|m|>1` (b) `m >1` `m >-1` (d) `|m|lt=1`

`|m|gt1`

`mgt1`

`mgt-1`

`|m|le1`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

APPLICATION OF DERIVATIVES
CENGAGE|Exercise Exercise (Multiple)|10 Videos
APPLICATION OF DERIVATIVES
CENGAGE|Exercise Exercise (Numerical)|12 Videos
APPLICATION OF DERIVATIVES
CENGAGE|Exercise Exercise 5.8|2 Videos
3D COORDINATION SYSTEM
CENGAGE|Exercise DPP 3.1|11 Videos
APPLICATION OF INTEGRALS
CENGAGE|Exercise Solved Examples And Exercises|17 Videos

Similar Questions

Explore conceptually related problems

The line y = mx + 1 is a tangent to the curve y^(2) = 4x if the value of m is

If m is the slope of a tangent to the hyperbola (x^(2))/(a^(2)-b^(2))-(y^(2))/(a^(3)-b^(3)) =1 where a gt b gt 1 when

If the slope of line through the origin which is tangent to the curve y=x^3+x+16 is m , then the value of m-4 is____.

If one of the lines of m y^2+(1-m^2)x y-m x^2=0 is a bisector of the angle between the lines x y=0 , then m is (a) 1 (b) 2 (c) -1/2 (d) -1

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+a)=0 , then

Prove that the equation of any tangent to the circle x^2+y^2-2x+4y-4=0 is of the form y=m(x-1)+3sqrt(1+m^2)-2.

If y+3=m_1(x+2) and y+3=m_2(x+2) are two tangents to the parabola y^2=8x , then

Consider the hyperbola H : x^2-y^2=1 and a circle S with center N(x_2,0) . Suppose that Ha n dS touch each other at a point P(x_1, y_1) with x_1>1 and y_1> 0. The common tangent to Ha n dS at P intersects the x-axis at point Mdot If (l ,m) is the centroid of the triangle P M N , then the correct expression(s) is (are) (d l)/(dx_1)=1-1/(3x1 2)forx_1>1 (d m)/(dx_1)=(x_1)/(3sqrt(x1 2-1)) for x_1> (d l)/(dx_1)=1+1/(3x1 2) for x_1>1 (d m)/(dy_1)=1/3 for x_1>0

The real value of a for which the value of m satisfying the equation (a^2-1)m^2-(2a-3)m+a=0 given the slope of a line parallel to the y-axis is (a) 3/2 (b) 0 (c) 1 (d) +-1

The values of 'm' for which a line with slope m is common tangent to the hyperbola x^2/a^2-y^2/b^2=1 and parabola y^2 = 4ax can lie in interval:

CENGAGE-APPLICATION OF DERIVATIVES-Exercise (Single)

The number of tangents to the curve x^(3/2)+y^(3/2)=2a^(3/2),a >0, whi...
Text Solution
|
The angle made by the tangent of the curve x=a(t+s in tcos t),y=a(1+s ...
Text Solution
|
If m is the slope of a tangent to the curve e^y=1+x^2, then |m|>1 (b)...
Text Solution
|
If at each point of the curve y=x^3-a x^2+x+1, the tangent is inclined...
Text Solution
|
The slope of the tangent to the curve y=sqrt(4-x^2) at the point where...
Text Solution
|
The curve given by x+y=e^(x y) has a tangent parallel to the y- axis a...
Text Solution
|
If the line joining the points (0,3)a n d(5,-2) is a tangent to the cu...
Text Solution
|
The distance between the origin and the tangent to the curve y=e^(2x)+...
Text Solution
|
The normal to the curve 2x^2+y^2=12 at the point (2,2) cuts the curve ...
Text Solution
|
At what point of curve y=2/3x^3+1/2x^2, the tangent makes equal angle ...
Text Solution
|
The equation of the tangent to the curve y=b e^(-x//a) at the point wh...
Text Solution
|
Then angle of intersection of the normal at the point (-5/(sqrt(2)),3/...
Text Solution
|
A function y-f(x) has a second-order derivative f^(x)=6(x-1)dot It its...
Text Solution
|
If x+4y=14 is a normal to the curve y^2=alphax^3-beta at (2,3), then t...
Text Solution
|
The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tan...
Text Solution
|
Let C be the curve y=x^3 (where x takes all real values). The tangent ...
Text Solution
|
The x-intercept of the tangent at any arbitrary point of the curve a/(...
Text Solution
|
Given g(x)=(x+2)/(x-1) and the line 3x+y-10=0. Then the line is (a)tan...
Text Solution
|
The number of point in the rectangle {(x , y)}-12lt=xlt=12a n d-3lt=yl...
Text Solution
|
Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) ...
Text Solution
|